# Gurobi Mex: A MATLAB interface for Gurobi

(Difference between revisions)
 Revision as of 10:46, 20 January 2010 (edit)m (→Example 2. Integer programming)← Previous diff Revision as of 01:50, 24 January 2010 (edit) (undo) (→Input Description)Next diff → Line 69: Line 69: * '''c''': objective coefficient vector, double. * '''c''': objective coefficient vector, double. + :Besides a vector, [] (empty array) means uniformly 0 coefficients, and ''scalar'' means all coefficients equal to ''scalar''. * '''objtype''': 1 (minimization) or -1 (maximization). * '''objtype''': 1 (minimization) or -1 (maximization). * '''A''': constraint coefficient matrix, double, sparse. * '''A''': constraint coefficient matrix, double, sparse. * '''b''': constraint right-hand side vector, double. * '''b''': constraint right-hand side vector, double. + : If a ''sparse'' vector is specified, it is converted to ''full''. This conversion takes time and memory space. * '''contypes''': constraint types. Char array of '>', '<', '='. * '''contypes''': constraint types. Char array of '>', '<', '='. - :Example: '>><=' means 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. :Warning: '>=' means two constraints instead of one an inequality constraint. :Warning: '>=' means two constraints instead of one an inequality constraint. - * '''lb''': variable lower bound vector, double. Empty means 0 lower bound. + :Example: '>><=' means 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. - * '''ub''': variable upper bound vector, double. Empty means no (or inf) upper bound. + :If a single character is specified, all constraints are uniformly signed to the corresponding type. - * '''vartypes''': variable types. Char array of chars 'C', 'B', 'I', 'S', 'N'. C for continuous; B for binary; I for integer; S for semi-continuous; N for semi-integer. Empty means all variables are continuous. + * '''lb''': variable lower bound vector, double. + :[] (empty array) means 0 lower bound. -inf means no lower bound. ''scalar'' means a uniform lower bound equal to ''scalar''. + * '''ub''': variable upper bound vector, double. + :[] (empty array) means no (or infinity) upper bound. ''scalar'' means a uniform upper bound equal to ''scalar''. + * '''vartypes''': variable types. Char array of chars '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' stands for five continuous variables. :Example: 'CCCCC' stands for five continuous variables. :Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined. :Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined. + :If a single character is specified, all variables are uniformly signed to the corresponding type. * '''options''': ''optional'' structure that may contain one or more of the following fields: (see [http://www.gurobi.com/html/doc/refman/node378.html Gurobi's parameter help] for their allowed values. Also, see [[Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Three_Examples|examples]] below.) * '''options''': ''optional'' structure that may contain one or more of the following fields: (see [http://www.gurobi.com/html/doc/refman/node378.html Gurobi's parameter help] for their allowed values. Also, see [[Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Three_Examples|examples]] below.) ** '''options.IterationLimit''': see Gurobi's parameter help ** '''options.IterationLimit''': see Gurobi's parameter help

## Revision as of 01:50, 24 January 2010

Gurobi Mex is a MATLAB interface for Gurobi 2 written by Wotao Yin. It calls Gurobi to solve linear/mixed-integer optimization problems. Gurobi is one of the leading linear and mixed integer programming solvers.

The 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, and its source code serves as a start point for those who want to develop a customized MATLAB interface for Gurobi.

Its current version is 1.05 published on Jan 2, 2010.

## Model

``` min/max  c'x

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

### History

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.

### Building Gurobi Mex in MATLAB

#### Under Windows

```mex -O -I"<gurobi include path>" gurobi_mex.c "<absolute path/gurobi20.lib>"
```

#### Under Unix

```mex -O -I"<gurobi include path>" gurobi_mex.c -L"<gurobi lib path>" -lgurobi20
```

#### Tested platforms

• Windows 32-bit and gcc (included in free Mingw/GnuMex)
• Ubuntu Linux 9.10 64-bit and gcc.

MATLAB's built-in lcc cannot link with Gurobi.

Please make sure the dynamic library of Gurobi 2.x is in system path.

## Syntax

x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes);
x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes, options);
[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.
Besides a vector, [] (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, sparse.
• b: constraint right-hand side vector, double.
If a sparse vector is specified, it is converted to full. This conversion takes time and memory space.
• contypes: constraint types. Char array of '>', '<', '='.
Warning: '>=' means two constraints instead of one an inequality constraint.
Example: '>><=' means 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, all constraints are uniformly signed to the corresponding type.
• lb: variable lower bound vector, double.
[] (empty array) means 0 lower bound. -inf means no lower bound. scalar means a uniform lower bound equal to scalar.
• ub: variable upper bound vector, double.
[] (empty array) means no (or infinity) upper bound. scalar means a uniform upper bound equal to scalar.
• vartypes: variable types. Char array of chars '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' stands for five continuous variables.
Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined.
If a single character is specified, all variables are uniformly signed to the corresponding type.
• options: optional structure that may contain one or more of the following fields: (see Gurobi's parameter help for their allowed values. Also, see examples below.)
• options.IterationLimit: see Gurobi's parameter help
• options.FeasibilityTol: see Gurobi's parameter help
• options.IntFeasTol: see Gurobi's parameter help
• options.OptimalityTol: see Gurobi's parameter help
• options.LPMethod: see Gurobi's parameter help
• options.Presolve: see Gurobi's parameter help
• options.Display: controls the level of screen output. 0 for no output; 1 for no output unless error; 2 (default) for normal output.
• options.UseLogfile: this field (no matter what value is assigned to it) lets Gurobi generate a log file. The file name is "gurobi_mex.log" by default. To change the name, modify field LOGFILENAME in the source file.
• options.WriteToFile: char array; contains 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:
• 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
• 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
• lambda: Lagrange multipliers. Because solving MIPs gives no such output, do not ask for this output for MIPs.

## Three 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.LPMethod = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.UseLogfile = [];      % as long as opts.UseLogfile exists, a log file is created
opts.WriteToFile = 'test_gurobi_mex_LP.mps';

[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: gurobi_mex.log. MPS file: test_gurobi_mex_LP.mps.

### Example 2. Integer programming

This example is borrowed from mip1_c.c of Gurobi 2.0.

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.LPMethod = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.UseLogfile = [];      % as long as opts.UseLogfile exists, a log file is created
opts.WriteToFile = 'test_gurobi_mex_MIP.mps';

[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: gurobi_mex.log. MPS file: test_gurobi_mex_MIP.mps.

### Example 3. Compressive sensing

See example m-file test_gurobi_mex_CS.m.

## Feedback

I would be delighted to hear from you if you find Gurobi Mex useful, or if you have any suggestions, contributions, or bug reports. Please send these to Wotao Yin (wotao.yin AT rice.edu)

## How to cite

Wotao Yin. Gurobi Mex: A MATLAB interface for Gurobi, URL: http://www.caam.rice.edu/~wy1/gurobi_mex, 2009-2010.