CONE World - Solvers

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Conic Programming Solvers

There are several cone programming solvers available, both free codes from research institutions and commercial codes from various vendors. The solvers differ in the methods they use, in the size of models they can handle, and in the format of models they accept.

CONOPT	Nonlinear optimization solver from ARKI Consulting and Development, Copenhagen, Denmark
CPLEX	High-performance linear, mixed-integer linear, and quadratic programming solver from ILOG.
LOQO	General purpose solver for smooth nonlinear programs from Princeton University.
MOSEK	Software package for the solution of linear, mixed-integer linear, and convex nonlinear mathematical optimization problems (including SOCP). From MOSEK ApS, Copenhagen, Denmark
SeDuMi	MATLAB toolbox for solving optimization problems over symmetric cones. From Tilburg University, Netherlands.
SDPT3	MATLAB software for semidefinite-quadratic-linear programming from the National University of Singapore.

Conic Programming Interfaces

This sections lists interfaces to conic programming solvers.

YALMIP YALMIP is an interface to a number of semi-definite and conic programming solvers and is developed by Johan Löfberg, ETH Zürich, Switzerland

Solver/Interface Descriptions

CONOPT

CONOPT is a large-scale nonlinear programming solver utilizing various methods (Steepest-Descent, Quasi-newton, SLP, SQP) and uses exact second derivatives. SOCP models are solved via NLP formulation without smoothing.

Language/Input Format: AIMMS, AMPL, FORTRAN, GAMS, LINGO, MATLAB/TOMLAB, MPL
Capabilities: CNS, DNLP, NLP, SOCP

For more information see http://www.gams.com/dd/docs/solvers/conopt.pdf.

CPLEX

CPLEX is a powerful Linear Programming (LP), Mixed-Integer Programming (MIP), Quadratically Constraint Programming (QCP) and second order cone programs, and Mixed-Integer Quadratically Constraint Programming (MIQCP) solver based on the Cplex Callable Library from the ILOG CPLEX Division.

LPs are solved via the following algorithms: Primal Simplex, Dual Simplex, Network, Barrier, and Sifting. MIPs are solved using an implementation of a branch-and-bound search with modern algorithmic features such as cuts and heuristics.

CPLEX transforms QCPs into SOCPs (Second Order Cone Programs) for the barrier solver. CPLEX also supports SOCPs inputted directly.

Language/Input Format: AIMMS, AMPL, C/C++, FORTRAN, GAMS, MATLAB/TOMLAB, MPL,
Capabilities: LP, MIP, QCP, MIQCP, SOCP

For more information see http://www.gams.com/dd/docs/solvers/cplex.pdf.

LOQO

LOQO is a software package for the solution of large scale smooth nonlinear programming problems. It can also handle SOCP and semi-definite programming (SDP) problems and utilizes an efficient interior point method. SOCP are solved via reformulation as smooth nonlinear programs.

Language/Input Format: AMPL, C, MATLAB, SDPA
Capabilities: NLP, SDP, SOCP

For more information, see http://www.orfe.princeton.edu/~loqo/.

MOSEK

MOSEK is a software package for the solution of linear, mixed-integer linear, and convex nonlinear mathematical optimization problems. MOSEK is particularly well suited for solving large-scale linear programs using an extremely efficient interior point algorithm. The interior point algorithm has many complex solver options which the user can specify to fine-tune the optimizer for a particular model.

Furthermore, MOSEK can solve generalized linear programs involving nonlinear conic constraints and convex nonlinear programs. In particular, the MOSEK conic optimizer implements the Nesterov-Todd search direction, as well as a Mehrotra type predictor-corrector extension and sparse linear algebra for computational efficiency.

Language/Input Format: AMPL, C, GAMS, MATLAB, QPS (extended MPS)
Capabilities: LP, MIP, NLP (convex), SOCP

Also see http://www.gams.com/dd/docs/solvers/mosek.pdf.

SeDuMi

Matlab toolbox for solving optimization problems over symmetric cones, i.e. it allows not only for linear constraints, but also quasiconvex-quadratic constraints and positive semi-definiteness constraints. SeDuMi incorporates a primal-dual interior point method and implements a self-dual minimization technique for optimization over symmetric cones. Iterative solutions are updated in product form which makes it possible to provide highly accurate solutions.

Complex valued entries are allowed. Both symbolic and numerical reordering schemes, Cholesky and pre-conditioned conjugate gradient techniques that balance speed/accuracy performance. Sophisticated dense column handling, using Goldfarb-Scheinberg product form idea. Proven polynomial worst case operation bound.

Language/Input Format: MATLAB, MATLAB+C,SDPA,SDPpack
Capabilities: LP, SDP, SOCP

Also see http://fewcal.kub.nl/sturm/software/sedumi.html.

SDPT3

MATLAB-based software that can incorporate FORTRAN or C subroutines via MEX files for faster execution. It implements an infeasible path-following algorithm for solving conic optimization problems involving semidefinite, second-order and linear cone constraints. Sparsity in the data is exploited whenever possible.

Language/Input Format: MATLAB+C or FORTRAN, SDPA
Capabilities: SDP, SOCP

Also see http://www.math.nus.edu.sg/~mattohkc/sdpt3.html.

YALMIP

YALMIP is a free MATLAB toolbox for rapid prototyping of optimization problems. The package initially aimed at the control community and focused on semidefinite programming, but the latest release extends this scope significantly.

The main features of YALMIP are:

Easy to install since it is entirely based on MATLAB code.
Easy to learn : 3 new commands is all the user needs to get started.
Easy to use : you define your constraints and objective functions using intuitive and standard MATLAB code.
Automatic categorization of problems, and automatic solver selection
Supports numerous external solvers, both free and commercial.

Language/Input Format: MATLAB
Capabilities: LP, QCP, MIP, SOCP, SDP, Multi-Parametric Programming, Geometric Programming

Also see http://control.ee.ethz.ch/~joloef/yalmip.msql.