# Gurobi Mex: A MATLAB interface for Gurobi

(Difference between revisions)

-                                                              min/max  c'x                                                                                                                                                                                                                                                                                                                                   +                                                                                          min/max  x'Cx + c'x

subject to                                                                                                                                                                                                                                                                                                                                                                                                                                subject to
-                                                              Ax  [>= / <= / =]  b,                                                                                                                                                                                                                                                                                                                          +                                                                                          Ax >= / <= / = b,
lb <= x <= ub,                                                                                                                                                                                                                                                                                                                                                                                                                            lb <= x <= ub,
-                                                              x(i) is [continuous / binary / integer / semi-continuous / semi-integer].                                                                                                                                                                                                                                                                      +                                                                                          SOS constraints,
+                                                                                          x(i) is continuous / binary / integer / semi-continuous / semi-integer.

+                                                                                          Find a solution or report infeasibility of
+
+                                                                                          5 x1 + 4 x2        + 5 x4 >= -21
+                                                                                          5 x1 + 3 x2 + 1 x3 + 4 x4  = -14
+                                                                                          3 x1 + 5 x2 + 2 x3 - 5 x4  =  11
+                                                                                          x1,x2,x3,x4 >= 0.
+
+ MATLAB code: +
+                                                                                          c = [];                    % use [] or 0 for null objective
+                                                                                          objtype = -1;              % 1 for minimize, -1 for maximize
+                                                                                          A =  sparse([5 4 0 5; 5 3 1 4; 3 5 2 -5]);
+                                                                                          b = [-21; -14; 11];
+                                                                                          lb = [];                   % stands for 0 lower bound uniformly
+                                                                                          ub = [];                   % stands for inf upper bound uniformly
+                                                                                          contypes = '>==';
+                                                                                          vtypes = [];               % same as vtypes = 'CCCC'
+
+                                                                                          clear opts
+                                                                                          opts.FeasibilityTol = 1e-6;
+                                                                                          opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
+                                                                                          opts.Display = 1;
+                                                                                          opts.LogFile = 'test_gurobi_mex_Feasibility.log';
+                                                                                          opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';  % this option can cause a long delay if problem is large
+
+                                                                                          [x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
+
+ + Results: +
+                                                                                          disp('Solution:');disp(x')
+                                                                                          disp('Optimal obj value:');disp(val)
+                                                                                          disp('Exit flag:');disp(exitflag)
+
+                                                                                          Model is infeasible. No solution will be returned.
+
+                                                                                          Solution:
+                                                                                          Optimal obj value:
+                                                                                          Exit flag:
+                                                                                          3
+
+ Log file: ''test_gurobi_mex_Feasibility.log''. MPS file: ''test_gurobi_mex_Feasibility.mps''. + + === Example 4. SOS constraint test === + Problem: +
+                                                                                          min –3 x1 – 1 x2 – 1 x3,
+
+                                                                                          subject to
+                                                                                          x1 + x2 + x3 <= 2,
+                                                                                          0 <= x1 <= 1, 0 <= x2 <= 1, 0 <= x3 <= 2,
+                                                                                          SOS type 1: x1 = 0 or x2 = 0,
+                                                                                          SOS type 1: x1 = 0 or x3 = 0.
+
+ MATLAB code: +
+                                                                                          c = [-3; -1; -1];
+                                                                                          objtype = 1;
+                                                                                          A =  sparse([1 1 1]);
+                                                                                          b = 2;
+                                                                                          lb = []; % means 0 lower bound
+                                                                                          ub = [1 1 2];
+                                                                                          contypes = '<';
+                                                                                          vtypes = []; % same as vtypes = 'CCC'
+                                                                                          sos.weights = sparse([1 1; 2 0; 0 2]);
+                                                                                          sos.types = int32([1 1]);   % Both the SOS constraints are of type 1
+
+                                                                                          clear opts
+                                                                                          opts.FeasibilityTol = 1e-6;
+                                                                                          opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
+                                                                                          opts.Display = 1;
+                                                                                          opts.LogFile = 'test_gurobi_mex_Feasibility.log';
+                                                                                          opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';
+
+                                                                                          [x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
+
+ + Results: +
+                                                                                          Optimal solution found (tolerance 1.00e-04)
+                                                                                          Best objective -3.0000000000e+00, best bound -3.0000000000e+00, gap 0.0%
+
+                                                                                          Solution:
+                                                                                          1     0     0
+
+ Log file: ''test_gurobi_mex_SOS.log''. MPS file: ''test_gurobi_mex_SOS.mps''. + + === Example 5. Quadratic programming === + This example appears in MATLAB Help entry for ''quadprog''. + + Problem: +
+                                                                                          min 0.5 x0^2 - x0*x1 + x1^2 - 2*x0 - 6*x1,
+
+                                                                                          subject to
+                                                                                          x0 +  x1 <= 2,
+                                                                                          -x0 + 2x1 <= 2,
+                                                                                          2x0 +  x1 <= 3,
+                                                                                          x0 >= 0, x1 >= 0.
+
+ MATLAB code: +
+                                                                                          clear opts
+
+                                                                                          c = [-2 -6];    % objective linear term
+                                                                                          objtype = 1;    % minimization
+                                                                                          A =  sparse([1 1; -1 2; 2 1]); % constraint coefficients
+                                                                                          b = [2; 2; 3];  % constraint right-hand side
+                                                                                          lb = [];        % [] means 0 lower bound
+                                                                                          ub = [];        % [] means inf upper bound
+                                                                                          contypes = '<<<'; % three <= inequalities
+                                                                                          vtypes = [];      % [] means all variables are continuous
+                                                                                          % note that 0.5 x0^2 - x0*x1 + x1^2 = 0.5 x0*x0 - x0*x1 + x1*x1
+                                                                                          opts.QP.qrow = int32([0 0 1]); % indices of leading   variables (x0), (x0), (x1) in 0.5 (x0)*x0 - (x0)*x1 + (x1)*x1
+                                                                                          opts.QP.qcol = int32([0 1 1]); % indices of following variables (x0), (x1), (x1) in 0.5 x0*(x0) - x0*(x1) + x1*(x1)
+                                                                                          opts.QP.qval = [0.5 -1 1];     % coefficients of 0.5 x0^2 - x0*x1 + x1^2
+
+                                                                                          opts.IterationLimit = 200;
+                                                                                          opts.FeasibilityTol = 1e-6;
+                                                                                          opts.IntFeasTol = 1e-5;
+                                                                                          opts.OptimalityTol = 1e-6;
+
+                                                                                          [x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
+
+                                                                                          disp('Solution:');disp(x')
+                                                                                          disp('Optimal obj value:');disp(val)
+                                                                                          disp('Exit flag:');disp(exitflag)
+                                                                                          disp('Optimization info:');disp(output)
+                                                                                          disp('Lagrange multiplers:');disp(lambda')
+
+ + Results: +
+                                                                                          Solution:
+                                                                                          0.6667    1.3333
+                                                                                          Optimal obj value:
+                                                                                          -8.2222
+                                                                                          Exit flag:
+                                                                                          2
+                                                                                          Optimization info:
+                                                                                          IterCount: 4
+                                                                                          Runtime: 0.0630
+                                                                                          ErrorMsg: []
+                                                                                          Lagrange multiplers:
+                                                                                          -3.1111   -0.4444         0
+

## Revision as of 15:40, 25 September 2012

Gurobi Mex is a free MATLAB interface for Gurobi 2, 3, and 4 written by Wotao Yin with contributions by Jon Dattorro, Imre Polik, and Tomáš Strnad. It calls Gurobi to solve linear/quadratic/mixed-integer optimization problems. Gurobi offers free trial and free academic license.

This interface is open source and subject to Creative Commons Attribution-Share Alike 3.0 United States License. It is a tool for MATLAB users to quickly call Gurobi. Its source code may also serve as a starting point for those who want to develop a customized MATLAB interface for Gurobi.

It is not trivial to write a good interface (it is about two thousand lines of code). If you find this interface useful, please credit it in your publications [bibtex] [Endnote] [text], as this will motivate the author to keep the interface up to date with the latest Gurobi, as well as improving its functions and making it easier to use.

## Model (LP, QP, MIP, MIQP)

``` min/max  x'Cx + c'x

subject to
Ax >= / <= / = b,
lb <= x <= ub,
SOS constraints,
x(i) is continuous / binary / integer / semi-continuous / semi-integer.
```

## Syntax

x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes);
x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes, opts);
[x,val] = gurobi_mex(...);
[x,val,flag] = gurobi_mex(...);
[x,val,flag,output] = gurobi_mex(...);
[x,val,flag,output,lambda] = gurobi_mex(...);

## Input Description

• c: objective coefficient vector, double type.
[] (empty array) means uniformly 0 coefficients, and scalar means all coefficients equal to scalar.
• objtype: 1 (minimization) or -1 (maximization).
• A: constraint coefficient matrix, double type, sparse.
• b: constraint right-hand side vector, double type.
Gurobi takes a dense vector for this input. If a sparse vector is specified, it will be converted to full by Gurobi Mex.
• contypes: constraint types. Char array of '>', '<', '='.
Warning: '>=' specifies two constraints, not one.
Example: '>><=' specifies four constraints. The first two constraints have greater or equal to signs, the third has less than or equal to sign, and the last is an equality constraint.
If a single character is specified, it will be applied to all constraints uniformly.
• lb: variable lower bound, double type, either scalar or vector.
[] (empty array) means 0 lower bound. -inf means no lower bound. If a scalar is specified, it will be the uniform lower bound for all variables.
• ub: variable upper bound, double type, either scalar or vector.
[] (empty array) means no (or infinity) upper bound. If a scalar is specified, it will be the uniform upper bound for all variables.
• vartypes: variable types, char array of 'C', 'B', 'I', 'S', 'N'. 'C' for continuous; 'B' for binary; 'I' for integer; 'S' for semi-continuous; 'N' for semi-integer. [] (empty array) means all variables are continuous.
Example: 'CCCCC' specifies five continuous variables.
Note that a semi-continuous variable is one that must be either zero or a value between its minimum and maximum. Semi-integer variables are similarly defined.
If a single character is specified, all variables will be signed to the corresponding type uniformly.

### Gurobi Parameters

• opts: optional structure that may have any number of following parameters.
• opts.[any Gurobi parameter]: See Gurobi Parameters for their allowed values.
• opts.QP: Quadratic objective terms. See here.
• opts.SOS: Special ordered set constraints. See here.
• opts.Start: MIP start vector, or Gurobi's attribute 'Start'. See here.
• opts.TrapCtrlC: true (to trap Ctrl-C) or false (not to trap Ctrl-C).
• opts.Display: screen output level. 0 (no output); 1 (version and error messages only); 2 (default output). For complete silence, set opts.DisplayInterval=0 and opts.OutputFlag=0 (to silence Gurobi) and opts.Display=0 (to make Gurobi Mex silent).
• opts.WriteToFile: char array of the name of the file to which optimization data is written. See Gurobi C-Reference entry GRBwrite for supported formats. This option helps one verify whether the model is correctly passed to Gurobi.

## Output Description

• x: primal solution vector; empty if Gurobi encounters errors or stops early (in this case, check output flag).
• val: optimal objective value; empty if Gurobi encounters errors or stops early.
• flag: value meanings:
• [ ] (empty 1x1 array) general failure
• 1 for not started
• 2 for optimal
• 3 for infeasible
• 4 for infeasible or unbounded
• 5 for unbounded
• 6 for objective worse than user-specified cutoff
• 7 for reaching iteration limit
• 8 for reaching node limit
• 9 for reaching time limit
• 10 for reaching solution limit
• 11 for user interruption
• 12 for numerical difficulties
• 13 for suboptimal solution (Gurobi 3 and later)
• output: structure contains the following fields
• output.IterCount: number of Simplex iterations
• output.Runtime: running time in seconds
• output.ErrorMsg: contains Gurobi error message, if any
• output.Versions.GurobiMex: version of this interface (supported by v1.61 and later)
• output.Versions.LibMajor, output.Versions.LibMinor, and output.Versions.LibTechi: Gurobi library version (supported by v1.61 and later)
• lambda: constraint dual variables (up to v1.50) or structure contains the following fields (v1.55 and later)
• lambda.RC: reduced cost
• lambda.Pi: constraint dual variables
• lambda.Slack: constraint slack variables

## Notes

Gurobi 4 and later solve quadratic programs. The quadratic terms in the objective function should be specified by opts.QP.qrow, opts.QP.qcol, and opts.QP.qval, which correspond to the input arguments qrow, qcol, and qval of function GRBaddqpterms. They are all 1D arrays. The first two arguments, qrow and qcol, specify the row and column indices (starting from 0) of 2nd-order terms such as $LaTeX: x_1^2$ and $LaTeX: x_1 x_2\,$. The third argument, qval, gives their coefficients. An example is given below.

To solve a quadratic program with no constraints, set A = [], b = [], and contypes = [].

### SOS Constraints

SOS stands for Special Ordered Sets. This mex program uses opts.SOS.weights and opts.SOS.types to pass SOS constraints to Gurobi. opts.SOS.weights is a sparse matrix describing the weights of SOS variables, and opts.SOS.types a 1D array of type int32 or int64 (if sizeof(int) is 4 for your system, then you should use int32; if 8, use int64), which specifies the constraint types. Here is an example with 4 variables and 3 SOS constraints:

```SOS1: x1 = 0 or x2 = 0
SOS1: x1 = 0 or x3 = 0
SOS2: (x1, x3, x2, x4)
```

The corresponding code for a 32-bit system is

``` opts.SOS.weights = sparse([
1 1 1;
2 0 3;
0 2 2;
0 0 4]);
opts.SOS.types = int32([1 1 2]);
```

The ith column of opts.SOS.weights specifies the weights (i.e., orders) of the variables in the ith SOS constraint.

### MIP Start Vector

To specify an MIP start vector (supported since v1.45), say x = [1 0 3 2], one can use one of the following two ways:

```opts.Start = [1 0 3 2];
```

or

```opts.Start.pos = int32([0 1 2 3]); % use int64 if sizeof(int) is 8 for your system
opts.Start.val = [1 0 3 2];
```

To specify start values for a subset of variables, for example to set x = [? ? -1 2], where ? means undefined, one can choose either one of the following two ways

```GRB_UNDEFINED = 1e101;
opts.Start = [GRB_UNDEFINED  GRB_UNDEFINED  -1 2];
```

or

```opts.Start.pos = int32([2 3]); % use int64 if sizeof(int) is 8 for your system
opts.Start.val = [-1 2];
```

### How to pass a parameter from MATLAB to Gurobi?

v1.35 and v1.45 support all parameters of Gurobi 3 and 4, respectively. However, if you want to specify a new or undocumented Gurobi parameter of your interest, you can DIY very easily. Suppose that we want to set a double-type parameter called SecretPara in MATLAB and pass it through this mex interface to Gurobi. Because the parameter TimeLimit has the same (double) type and it is already supported by this mex program, we can copy the code for TimeLimit, replace TimeLimit by SecretPara in the code, and paste it at Line 1250 of v1.35 (or Line 510 of v1.30), just before the mex program checks unrecognized input option fields. After compiling gurobi.c, the modified mex will let you assign a double value to opts.SecretPara. We compare the code for TimeLimit and SecretPara below where the differences are italicized:

```       /* Option TimeLimit */
field_n = mxGetFieldNumber(IN_OPTS, "TimeLimit");
if (field_n != -1) {
field = mxGetFieldByNumber(IN_OPTS,0,field_n);
bOpts[field_n] = true;
if (!mxIsDouble(field) || mxIsComplex(field) || mxIsEmpty(field)) {
mexPrintf("Option TimeLimit must be real positive double (0 to inf).");
goto QUIT;
}
error = GRBsetdblparam(env, "TimeLimit", mxGetScalar(field));
if (error) goto QUIT;
}
```
```       /* Option SecretPara */
field_n = mxGetFieldNumber(IN_OPTS, "SecretPara");
if (field_n != -1) {
field = mxGetFieldByNumber(IN_OPTS,0,field_n);
bOpts[field_n] = true;
if (!mxIsDouble(field) || mxIsComplex(field) || mxIsEmpty(field)) {
mexPrintf("Option SecretPara must real double (?? through ??).");
goto QUIT;
}
error = GRBsetdblparam(env, "SecretPara", mxGetScalar(field));
if (error) goto QUIT;
}
```

Note that you must start from a parameter of the same type (int, double, or string). In case memory allocation is needed, use mxCalloc and make sure that mxFree has been called whenever the mex program exits, normally or not.

## Callbacks

Callbacks are useful to obtain the progress of Gurobi (e.g., by calling GRBcbget) and to modify its behavior during runtime (e.g., by calling GRBcbcut and GRBcbsolution).

Gurobi Mex implements a callback function mycallback to obtain Gurobi's progress messages and print them on the MATLAB screen. The print frequency is set in opts.DisplayInterval (in seconds). The same function is also used to detect user input Ctrl-C.

Information for Gurobi callbacks can be found here in Gurobi's help. An example can be found here.

## Examples

### Example 1. Linear programming

This example is borrowed from MATLAB's linprog help.

Problem:

``` min –5 x1 – 4 x2 –6 x3,

subject to
x1 – x2 + x3 ≤ 20
3 x1 + 2 x2 + 4 x3 ≤ 42
3 x1 + 2 x2 ≤ 30
0 ≤ x1, 0 ≤ x2, 0 ≤ x3.
```

MATLAB code:

``` c = [-5; -4; -6];
objtype = 1;
A =  sparse([1 -1  1; 3  2  4; 3  2  0]);
b = [20; 42; 30];
lb = zeros(3,1);           % same as lb = [];
ub = [];
contypes = '<<<';
vtypes = [];               % same as vtypes = 'CCC'; [] means 'C...C'

clear opts
opts.IterationLimit = 20;
opts.FeasibilityTol = 1e-6;
opts.IntFeasTol = 1e-5;
opts.OptimalityTol = 1e-6;
opts.Method = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_LP.log';     % optional
opts.WriteToFile = 'test_gurobi_mex_LP.mps'; % optional; it can cause a long delay if problem is large

[x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Results:

``` x' =
0 15 3

val =
-78

exitflag =
2

output =
IterCount: 2
Runtime: 0
ErrorMsg: []

lambda' =
0   -1.5000   -0.5000
```

Log file: test_gurobi_mex_LP.log. MPS file: test_gurobi_mex_LP.mps.

### Example 2. Integer programming

This example is borrowed from mip1_c.c of Gurobi 2.

Problem:

``` max  x + y + 2z,

subject to
x + 2 y + 3 z <= 4
x +   y       >= 1
x, y, z binary.
```

MATLAB code:

``` c = [1; 1; 2];
objtype = -1;              % 1 for minimize, -1 for maximize
A =  sparse([1 2 3; 1 1 0]);
b = [4; 1];
lb = [];
ub = [];
contypes = '<>';
vtypes = 'BBB';

clear opts
opts.IterationLimit = 20;
opts.FeasibilityTol = 1e-6;
opts.IntFeasTol = 1e-5;
opts.OptimalityTol = 1e-6;
opts.Method = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_MIP.log';
opts.WriteToFile = 'test_gurobi_mex_MIP.mps';  % this option can cause a long delay if problem is large

[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Gurobi does not give lambda (Pi, or Lagrange multipliers) for MIPs, unless model fix is called.

Results:

``` disp('Solution:');disp(x')
disp('Optimal obj value:');disp(val)
disp('Exit flag:');disp(exitflag)
disp('Optimization info:');disp(output)

Solution:
1     0     1

Optimal obj value:
3

Exit flag:
2

Optimization info:
IterCount: 0
Runtime: 0
ErrorMsg: []
```

Log file: test_gurobi_mex_MIP.log. MPS file: test_gurobi_mex_MIP.mps.

### Example 3. Feasibility test

Problem:

```Find a solution or report infeasibility of

5 x1 + 4 x2        + 5 x4 >= -21
5 x1 + 3 x2 + 1 x3 + 4 x4  = -14
3 x1 + 5 x2 + 2 x3 - 5 x4  =  11
x1,x2,x3,x4 >= 0.
```

MATLAB code:

``` c = [];                    % use [] or 0 for null objective
objtype = -1;              % 1 for minimize, -1 for maximize
A =  sparse([5 4 0 5; 5 3 1 4; 3 5 2 -5]);
b = [-21; -14; 11];
lb = [];                   % stands for 0 lower bound uniformly
ub = [];                   % stands for inf upper bound uniformly
contypes = '>==';
vtypes = [];               % same as vtypes = 'CCCC'

clear opts
opts.FeasibilityTol = 1e-6;
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_Feasibility.log';
opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';  % this option can cause a long delay if problem is large

[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Results:

``` disp('Solution:');disp(x')
disp('Optimal obj value:');disp(val)
disp('Exit flag:');disp(exitflag)

Model is infeasible. No solution will be returned.

Solution:
Optimal obj value:
Exit flag:
3
```

Log file: test_gurobi_mex_Feasibility.log. MPS file: test_gurobi_mex_Feasibility.mps.

### Example 4. SOS constraint test

Problem:

```min –3 x1 – 1 x2 – 1 x3,

subject to
x1 + x2 + x3 <= 2,
0 <= x1 <= 1, 0 <= x2 <= 1, 0 <= x3 <= 2,
SOS type 1: x1 = 0 or x2 = 0,
SOS type 1: x1 = 0 or x3 = 0.
```

MATLAB code:

``` c = [-3; -1; -1];
objtype = 1;
A =  sparse([1 1 1]);
b = 2;
lb = []; % means 0 lower bound
ub = [1 1 2];
contypes = '<';
vtypes = []; % same as vtypes = 'CCC'
sos.weights = sparse([1 1; 2 0; 0 2]);
sos.types = int32([1 1]);   % Both the SOS constraints are of type 1

clear opts
opts.FeasibilityTol = 1e-6;
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_Feasibility.log';
opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';

[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Results:

``` Optimal solution found (tolerance 1.00e-04)
Best objective -3.0000000000e+00, best bound -3.0000000000e+00, gap 0.0%

Solution:
1     0     0
```

Log file: test_gurobi_mex_SOS.log. MPS file: test_gurobi_mex_SOS.mps.

This example appears in MATLAB Help entry for quadprog.

Problem:

```min 0.5 x0^2 - x0*x1 + x1^2 - 2*x0 - 6*x1,

subject to
x0 +  x1 <= 2,
-x0 + 2x1 <= 2,
2x0 +  x1 <= 3,
x0 >= 0, x1 >= 0.
```

MATLAB code:

``` clear opts

c = [-2 -6];    % objective linear term
objtype = 1;    % minimization
A =  sparse([1 1; -1 2; 2 1]); % constraint coefficients
b = [2; 2; 3];  % constraint right-hand side
lb = [];        % [] means 0 lower bound
ub = [];        % [] means inf upper bound
contypes = '<<<'; % three <= inequalities
vtypes = [];      % [] means all variables are continuous
% note that 0.5 x0^2 - x0*x1 + x1^2 = 0.5 x0*x0 - x0*x1 + x1*x1
opts.QP.qrow = int32([0 0 1]); % indices of leading   variables (x0), (x0), (x1) in 0.5 (x0)*x0 - (x0)*x1 + (x1)*x1
opts.QP.qcol = int32([0 1 1]); % indices of following variables (x0), (x1), (x1) in 0.5 x0*(x0) - x0*(x1) + x1*(x1)
opts.QP.qval = [0.5 -1 1];     % coefficients of 0.5 x0^2 - x0*x1 + x1^2

opts.IterationLimit = 200;
opts.FeasibilityTol = 1e-6;
opts.IntFeasTol = 1e-5;
opts.OptimalityTol = 1e-6;

[x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);

disp('Solution:');disp(x')
disp('Optimal obj value:');disp(val)
disp('Exit flag:');disp(exitflag)
disp('Optimization info:');disp(output)
disp('Lagrange multiplers:');disp(lambda')
```

Results:

``` Solution:
0.6667    1.3333
Optimal obj value:
-8.2222
Exit flag:
2
Optimization info:
IterCount: 4
Runtime: 0.0630
ErrorMsg: []
Lagrange multiplers:
-3.1111   -0.4444         0
```

### Example 6. Mixed integer quadratic programming

See example m-file test_gurobi_mex_MIQP.m.

### Example 7. Compressive sensing

See example m-file test_gurobi_mex_CS.m.

## Feedback

Wotao Yin would be delighted to hear from you if you find Gurobi Mex useful, or if you have any suggestions, contributions, or bug reports.

Updated 4th output argument to make it easy to access version numbers.

### History

v1.60 (Gurobi 4) New features: support four new attributes introduced in Gurobi v4.6: Sifting, SiftMethod, ZeroObjNodes, and PreSparsify; versions of Gurobi library and this interface are displayed and returned.

v1.55 (Gurobi 4) New features: support the new options introduced in Gurobi v4.5; support the output of reduced costs and constraint slacks.

v1.50 (Gurobi 4) New features: quadratic programming with no linear constraints. Fixed bugs on handling SOS constraints on 64-bit systems.

v1.45 (Gurobi 4) New features: quadratic programming, MIP start vector. Fixed a bug on reporting unsupported options. Dattorro added support for all Gurobi options. Gurobi 4 changed parameter name "LPMethod" to "Method".

v1.35 (Gurobi 2&3) New features: support of Special Ordered Sets (SOS) constraints of types 1 and 2; support all Gurobi parameters and a new option TrapCtrlC; detection of unrecognized options. Fixed minor display issues. Dattorro added support for all Gurobi options.

v1.30 Short release for SOS support.

v1.20 New features: Ctrl-C detection, Gurobi 3 support. Improved error and exception handling. Empty array [] is returned if an output argument is not available. Fixed the display interval option.

v1.10 New features: callback, runtime progress output, flexible log file, flexible input types, more options. Part of the code was contributed by Tomáš Strnad. Known bug: print an empty line even if options DisplayInterval and Display are both set to 0. Fix: remove Line 736 of gurobi_mex.c: mexPrintf("\n");

v1.05 Major bug fix: char array of constraint sense has been fixed

v1.04 support writing model to files in various formats such as MPS, REW, LP, ...

v1.03 support log file

v1.02 fixed a memory leak issue

v1.01 update: support output dual solution lambda; allow vartypes to be empty (for all continuous variables).

v1.00 initial version.

### Install Gurobi Mex in MATLAB

#### Step 1. Install Gurobi

Download and install Gurobi. Refer to Gurobi's installation guide. Make sure that (i) proper environment variables are set, and (ii) your copy of Gurobi has a valid license.

#### Step 2. Install C++ Compiler

Download and install a supported C/C++ compiler for your copy of MATLAB. Do not use the built-in compiler lcc, which cannot link with Gurobi's library. A list of compatible compilers can be found here.

For Linux and Mac, gcc is a typical choice. Mac users can get gcc in Apple Xcode.

For Windows, one can use Microsoft's Visual C++ compiler. It is included in the free Microsoft Visual C++ Express (MSVC Express).

On 64-bit Windows, both MSVC Express and Windows SDK are needed. Google for "Windows SDK" and you will find a Microsoft webpage from where you can download and install the SDK (7.1 is the latest version as of Spring 2012). Only the compiler, headers and library, and .NET parts of the SDK are needed. An example can be found here.

Once a compiler is installed, run mex -setup in MATLAB, which shall automatically locates a compiler and generates a configuration file.

#### Step 3. Compiling Gurobi Mex

Automated compiling (still under test; your feedback is welcome): download this zip-file and unzip in the same folder of gurobi_mex.c. In MATLAB, run compile_mex and then gurobi_mex. If no error, congratulations! You are good to go.

In MATLAB, go to the folder where gurobi_mex.c is saved and call mex as follows:

##### Step 3a. Windows
```mex -O -I"<gurobi include path>" "<gurobi_mex.c>" "<gurobi C library file>" "<MATLAB libut.lib>"
```

For 64-bit MATLAB, add option "-largeArrayDims".

Example with Gurobi 4.51, MSVC2010 Express, MATLAB 2011a, and 64-bit Windows:

```mex -O -largeArrayDims -I"C:\Gurobi451\win64\include" "C:\folder\gurobi_mex.c"...
"C:\Gurobi451\win64\lib\gurobi45.lib" "C:\Program Files\MATLAB\R2011a\extern\lib\win64\microsoft\libut.lib"
```

Example with Gurobi 4.52, MSVC2010 Express, MATLAB 2011a, and 32-bit Windows:

```mex -O -I"C:\Gurobi452\win32\include" "C:\folder\gurobi_mex.c" "C:\Gurobi452\win32\lib\gurobi45.lib"...
"C:\Program Files\MATLAB\R2011a\extern\lib\win32\microsoft\libut.lib"
```
##### Missing libut.lib?

Ctrl-C detection requires libut.lib. If it is not found under your copy of MATLAB, you can download one for 32-bit Windows and 64-bit Windows (courtesy of Imre Polik).

Alternatively, libut.lib can be manually generated by creating a .def text file including the following five lines

```LIBRARY libut.dll
EXPORTS
utIsInterruptPending
utSetInterruptPending
[empty line]
```

and then calling lib.exe (included in MSVC) like

```"C:\Program Files\Microsoft Visual Studio 9.0\VC\bin\lib" /def:libut.def /out:libut.lib /machine:x86
```

where /machine:x86 should be replaced by /machine:x64 for 64-bit Windows.

##### Step 3b. Linux/Unix/OS X
```mex -O -I"<gurobi include path>" "<gurobi_mex.c>" -L"<gurobi lib path>" -l<gurobi C library file> -lut
```

For 64-bit MATLAB, add option "-largeArrayDims".

Example with Gurobi 3, GCC, MATLAB 2009B, and 64-bit Linux

```mex -O -I"/opt/gurobi300/linux64/include" "/home/wotao/gurobi mex/gurobi_mex.c" -L"/opt/gurobi300/linux64/lib" -lgurobi30 -lut -largeArrayDims
```

For OS X, see http://www.mathworks.com/support/solutions/en/data/1-FR6LXJ/ for a patch. This patch fixes general problems with mex for Mac.

#### Tested platforms

• 64-bit Ubuntu Linux 9.10, 64-bit MATLAB, and gcc.
• 32-bit Windows, 32-bit MATLAB, and gcc (part of free Mingw/GnuMex, alternatively TDM-GCC).
• 32-bit Windows, 32-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free).
• 64-bit Windows, 64-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free). Courtesy of Imre Polik.
• 64-bit Windows, 64-bit MATLAB, and MSVC 2010 Express.
• 64-bit OS-X Lion (10.7.5), 64-bit MATLAB, and gcc (required patch: http://www.mathworks.com/support/solutions/en/data/1-FR6LXJ/)

For 64-bit MATLAB, Jon Dattorro suggests a bug fix.

## FAQs

### compiling is successful, but gurobi_mex cannot run

Solution: check and correct Gurobi license and environment variables

Step 1. Check and validate Gurobi license

Step 2. Check system environment variables for Gurobi

Step 3. Verify MATLAB knows the correct system environment variables by running

```>> getenv('GUROBI_HOME')
>> getenv('PATH')
>> getenv('LD_LIBRARY_PATH') % on Unix/Linux/Mac
```

You may need to restart MATLAB from the terminal to get all environment variables loaded to MATLAB.

### "int32" or "int64" errors

Solution: use int32 if sizeof(int) is 4 for your system; use int64 if sizeof(int) is 8. To determine sizeof(int), take the following steps

Step 1. create "check_sizeof_int.c" with the following lines

```#include "mex.h"
void mexFunction(
int nlhs,       mxArray *plhs[],
int nrhs, const mxArray *prhs[]
)
{
mexPrintf("Size of int is %d\n", sizeof(int));
return;
}
```

Step 2. Launch Matlab, run mex check_sizeof_int.c, and then run check_sizeof_int

### MATLAB reports "out of memory"

Solution: run clear mex after each call to gurobi_mex

Running out of memory is often the result of memory leaks. However, the interface has been checked numerous times for memory leaks. If there still appears to be a leak, we are not sure if it is with the interface, Gurobi, or MATLAB itself.

### Gurobi Mex in a loop returns incorrect solutions

Try: double check whether the fields of opts are correctly updated in the loop; one often forgets cleaning up some fields, so data in the previous iteration is inadvertently used the new iteration. if not work

Try: use opts.WriteToFile=my_data.mps to generate data files and inspect the input data for errors. if not work

Then Try: run clear mex after each call to gurobi_mex