Home
Wikimization
Contact Us
Accumulator error feedback
CVX Download
Calculus of Inequalities
Rick Chartrand
Chromosome Structure EDM
Complementarity problem
Compressive Sampling
Compressed Sensing
Conic Independence
Convex Cones
Convex Functions
Convex Geometry
Convex, Affine, Conic: Hulls
Convex Iteration
Convex Optimization
Convex Optimization Group
Dattorro PC Optimization
Dattorro Supercomputer
Distance Geometry
Distance Matrix Cone
Dual Cones
Duality Gap
Eigenvalues/Eigenvectors
Elliptope and Fantope
Euclidean Distance Matrices
EDM cone faces
Extreme Directions
Face Recognition
Farkas Lemma
Fermat point
Fifth Metric Property
Jensen's Inequality
Jobs in Optimization
Kissing Number
Harold W. Kuhn
Linear Algebra
Linear Matrix Inequality
Manifold Learning
MATLAB for Optimization
Matrix Calculus
Molecular Conformation
Moreau's theorem
Isaac Newton
Angelia Nedic
Open Problems
Positive Matrix Factorization
Positive Semidefinite Cone
Projection
Projection on Cone
Proximity Problems
PY4SCIENCE
Quasiconvex Functions
Rank Constraint
Rockafellar
Justin Romberg
Michael Saunders
Schoenberg Criterion
Semidefinite Programming
Sensor Network Localization
Smallest Simplex
Systems Optimization Lab
Stanford SOL
Talks on Optimization
Joshua Trzasko
Video
Wikimization     Meboo     SOL      Video     CVX     Contact     
Felice crystal
Home arrow Semidefinite Programming
Semidefinite Programming

"Still, we are surprised to see the relatively small number of submissions to semidefinite programming (SDP) solvers, as this is an area of significant current interest to the optimization community.  We speculate that semidefinite programming is simply experiencing the fate of most new areas: Users have yet to understand how to pose their problems as semidefinite programs, and the lack of support for SDP solvers in popular modelling languages likely discourages submissions."

      positive semidefinite cone analogue

In broad terms, a semidefinite program is a convex optimization problem that is solved over a convex cone that is the positive semidefinite cone.

Semidefinite programming has emerged recently to prominence primarily because it admits a new class of problem previously unsolvable by convex optimization techniques, secondarily because it theoretically subsumes other convex techniques such as linear, quadratic, and second-order cone programming.  Determination of the Riemann mapping function from complex analysis, for example, can be posed as a semidefinite program.

If one were faced with the choice of implementing a problem as a semidefinite program or as a linear program, one should always choose the linear program.  The reason has only to do with contemporary implementation.  Nearly all semidefinite program solvers employ an interior-point method of solution (eg, a log barrier method).  The outcome of these techniques is to reduce relative numerical precision of an optimal solution to no more than 1E-8, whereas linear programs achieve 1E-15 accuracy.  Most researchers regard poor accuracy as an insignificant problem.  But we disagree - our methods for constraining rank are suffering limitations as a consequence. (confer  IEEE floating point)

Read more...
 
Course,   Video
Convex Optimization
     convex optimization
Stephen Boyd 
L. Vandenberghe 


Dattorro      convex optimization Euclidean distance geometry 2ε
Dattorro


Course
Bertsekas
     books by Bertsekas
Dimitri Bertsekas 


See Inside Hiriart-Urruty & Lemaréchal
Hiriart-Urruty
& Lemaréchal


See Inside
Rockafellar Rockafellar