The Problem:

min f(x) subject to h(x)=0, g(x)>=0,

n=dim(x), m=dim(g), p=dim(h).

The picture shows feasible domain and level sets for

f(x)=x_{1}^2+x_{2}^2,

g(x)=(x_{1}^2-x_{2},x_{2}^2-x_{1}) .

Infeasible points are shown in dark brown and the levels of f are shown in the feasible domain.

You'll find several sections:

The LP-problem, also mixed integer and stochastic

The QP-problem, also mixed integer

Semidefinite and second-order cone programming

Geometric programming

Robust Optimization

The general nonlinear problem (dense, sparse, nonsmooth, SIP)

Mixed integer nonlinear programming

Network constraints

Special/constraint solvers

Control problems

other collections/problems

**The LP-problem: f, g, h linear in x**

The LP-problem is often very high-dimensional. Several tools are necessary to deal with such problems. Some are listed here:

plam |
A free MILP modeling environment using lp_solve as MILP solver and SWI-Prolog |

MPS |
The description of the most widely used LP input format |

MPSreader |
An MPS reader for Windows |

QSreader |
a utility to convert this LP format to (and from) MPS; Windows/Unix executables |

lp2mps |
a utility (extracted from lp_solve) to convert the simple LP format to (and from) MPS |

ABACUS |
A general branch&cut library with mixed integer capability (C++) |

The following simplex-based solvers allow some or all of the variables to be constrained to attain integer values; all allow input in MPS format:

SCIP |
Framework for Constraint Integer Programming, links to CPLEX, SOPLEX, or CLP as LP solver (C) |

MIPCL |
MIP solver including modeling tools (C++, simplified version in Python) |

lp_solve |
C source, various binaries, and interfaces |

Pascal-MILP-solver |
Borland-Pascal sources, DOS/WIN binaries |

BonsaiG |
C, B&B, dynamic LP, partial arc consistency algorithm, binaries |

MOMIP |
B&B&cut, Win95 binary,binaries |

PICO (part of ACRO) |
B&C, using CPLEX, GLPK, or SOPLEX; AMPL interface |

MOSEK |
Simplex/IPM, Matlab, AMPL, GAMS interfaces, student license |

GLPK |
GNU LP library, B&B, dual/revised simplex, interior point, C, Windows-executables, Matlab interface, Java interface. R interface, Python interface |

CBC |
Simple branch&cut solver, part of COIN-OR (C++) |

SYMPHONY |
callable library for solving mixed-integer linear programs, uses Clp as default LP solver (C) |

MATLOG |
(MATLAB) The milp.m solver (needs lp.m from Matlab optimization toolbox) |

SCIL |
Symbolic Constraints in Integer Linear programming (C++) |

FEASPUMP |
The Feasibility Pump for finding a feasible solution; needs CPLEX (C++) |

MIPTS |
Tabu search heuristic for MIP; MPS, AMPL, CPLEX-LP input (C) |

PURE LP SOLVERS: most allow input in MPS format:

CLP |
the COIN LP code, simplex (C++) |

PyCOIN |
Python interface to CLP (maybe more COIN solvers) |

QSopt |
Simplex based; executables, library for Windows/Unix, free for research&education, Concorde interface, Mex interface |

SOPLEX |
Simplex based, C++ |

BPMPD |
interior point method, Win32-version, Unix-binaries (version 2.21), Unix-libraries (version 2.21), BPMPD_MEX, netlib-source (version 2.11, f77), C-version (version 2.11, f2c), AMPL interface |

HOPDM |
local version of code (interior point method using predictor-corrector-steps of higher order), HOPDM_C (f2c-converted version, includes f2c-library), IIASA-archive (C++/f77, dynamic memory allocation, binaries for Solaris and win95 only) |

PCx |
interior point method, f77/C, binaries for major platforms |

LOQO |
interior point method, C, student binaries, executables for major platforms, work for two months w/o license, AMPL interface, Matlab interface |

COPL-LP |
interior point method, includes crossover, DOS executable, HP binary, Linux binary |

LIPSOL |
interior point method, also MAT or LPP formats (Matlab) |

IPO/SIMPO |
interior and simplex LP-solver published in conjunction with Vanderbei's book, C |

PCLP |
predictor-corrector interior point code, SciLab or Matlab |

SPHSLFBF |
homogeneous self-dual interior point code, Matlab |

MINOS |
the long standing simplex based REFERENCE-implementation |

MCMA |
Multi-objective LP (Win95 and Solaris binaries only, includes tutorial models, based on HOPDM and MOMIP) |

reducedLP |
Constraint reduction for linear programs with many inequality constraints; paper and Matlab file |

rMPC |
Matlab interior point code specifically for LPs with many inequality constraints such as from a fine discretization of a semi-infinite LP |

MibS |
Mixed integer bilevel linear program code |

**Polyhedral Codes**

CDD |
Polyhedral codes in C/C++ |

CDDMEX |
Matlab interface to CDD |

LRS |
Polyhedral codes in C |

More polyhedral codes |
Avis's list |

Polyhedral FAQ |
Komei Fukuda's explanations |

**Exact LP Solvers**

EXLP |
Rational (exact) primal/dual simplex solver; needs GNU MP (C) |

Soplex |
Simplex solver using exact rational LU factorization and continued fraction approximations (C++) |

QSopt-Exact |
Rational (exact) primal/dual simplex solver; libraries, executables (C) |

**Stochastic LP Solvers**

Most accept input in SMPS format

SMPS reader |
by Gus Gassman, in f90 |

det2sto |
Downloadable Perl script to generate deterministic equivalent in AMPL format; websubmission |

MSLiP |
A Multistage Stochastic Linear Programming Code, available for research and teaching purposes |

BNBS |
for multi-stage problems, uses CPLEX, SOPLEX, or GLPK as LP solver (C/C++) |

SLP-IOR |
based on GAMS, large solver library, free for academic use |

**Stochastic MILP Solvers**

DDSIP |
Dual decomposition in two-stage stochastic mixed-integer programming, needs CPLEX lib (GPL, C) |

DSP |
Dual and Benders decomposition, uses Julia, MPI parallel |

**The QP problem: f quadratic, (non)convex, g, h linear**

Only bound constraints:

gpcg |
More&Toraldo's method combining cg with gradient projection |

MINQ |
General definite and bound constrained indefinite quadratic programming (in Matlab) |

Only equality constraints (** m = 0**):

toms/559 |
also for nonconvex f, provided the projected Hessian is positive definite |

**n** not too large, strictly convex

FORCES-pro |
a code generation tool for embedded convex QP (C, MATLAB, Simulink and Python interfaces available), free academic license |

qpOASES |
online active set solver, works well for model predictive control (C++, Matlab/R/SciLab interfaces) |

HPMPC |
Library for High-Performance implementation of solvers for MPC, highly optimized for common architectures; C, Octave interface |

dualqp |
f77 version of Spellucci's Goldfarb-Idnani dual QP solver |

QPC |
Active set and interior point, in C, callable from Matlab |

QuadProg++ |
C++ code for Goldfarb-Idnani dual QP |

QP_solver |
exact QP solver, part of CGAL (C++) |

**n** not too large, not necessarily convex

NewtonKKTqp |
indefinite QP solver, interior point (Matlab) |

IQP |
indefinite QP package (in Port lib) |

SPSOLQP |
indefinite QP solver, interior point (Matlab) |

QuadProgBB |
indefinite QP solver, Matlab/MEX |

**n** large

QPS (ext. MPS format) |
from BPMPD |

CONV_QP |
various methods for sparse convex QP (f77) |

MSS |
Matlab software for large-scale trust-region subproblems |

LSTRS |
Matlab software for large-scale trust-region subproblems and regularization |

COPL_QP |
interior point, convex problems, C, ext. MPS input, user's guide |

BPMPD |
convex problems, ext. MPS input, Win-95 version, BPMPD_MEX, Unix-libraries, Unix-binaries |

MOSEK |
interior point, Win, Linux binaries, ext. MPS input including quadratic constraints or through Matlab, student license |

OOQP |
object oriented C++ package, interior point, convex problems, needs MA27/57 from HSL archive |

GALAHAD |
QPA/QPB active set and IPM solvers, AMPL and ext. MPS(SIF) input |

HOPDM |
extension of LP-code, convex problems, ext. MPS input |

LOQO |
interior point method, C, executables for major platforms, work for several months w/o license, AMPL interface, Matlab interface |

RAL-QP |
more QP codes (from the NA group at Rutherford Appleton Labs) |

Software for specific quadratic programming problems:

GPDT |
Parallel Gradient Projection-based Decomposition Technique for SVM, also serial, Linux binary & C++ source |

OptiML |
f77 and C++ software for 2-norm soft margin SVM plus C++ code for the sparse inverse covariance problem |

OOQP |
C++ package includes solver for SVM and Huber regression problems |

Mixed integer quadratic programming:

MIQPBB |
branch&bound code |

PICOS |
Python Interface for Conic Optimization Solvers |

YALMIP |
Matlab toolbox for rapid prototyping of optimization problems, supports many solvers; B&B for mixed integer problems |

MIQP |
0-1 only, needs LP/QP solver, e.g. linprog/quadprog, part of MPT (Matlab) |

MOSEK |
ext. MPS input, Win, Linux, Solaris binaries, Matlab, quadratic constraints, student license |

**SDP&SOCP (semidefinite and second-order cone programming)**

Cone World initiative by GAMS

Linear semidefinite programming (SDP) solvers

SparseCoLo |
Matlab package for exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion |

SMCP |
Python Extension for Sparse Matrix Cone Programs |

ConicBundle |
A bundle method for minimizing the sum of convex functions given by oracles or from Lagrangian relaxation (C++, GPL) |

SDPHA |
A Matlab package for a homogeneous primal-dual method |

CSDP |
A library for semidefinite programming, predictor-corrector version of algorithm by Helmberg, Rendl, Vanderbei, and Wolkowicz (C) |

DSDP |
Dual-scaling algorithm (C, Matlab interface, parallel version) |

SDPA |
Solves semidefinite programs utilizing a Mehrotra-type predictor-corrector step, uses sparse matrix structure, includes documentation (C++), Matlab and MPI parallel versions |

SDPNAL+ |
MATLAB software for semidefinite programming with bound constraints |

PENSDP |
Penalty/barrier method for linear semidefinite programming, SDPA format input, |

SDPLR |
solves large-scale SDP problems (C) |

MPRW |
Boundary Point Method, Random SDP generators (Matlab) |

VSDP |
Matlab package for verified SDP. Needs INTLAB and SDPT3 or SDPA. |

MAXDET |
Software for Determinant Maximization Problems (C; Matlab interface) |

rmd |
Rigorous MAXDET; wrapper for above code (C++) |

CUTSDP |
A Toolbox for a Cutting-Plane Approach Based on Semidefinite Programming (C) |

Nonlinear semidefinite programming (SDP) solvers

PENLAB |
Open source version of PENNON, also for NLP (Matlab) |

PENBMI |
Program for problems with quadratic objective and bilinear matrix inequality constraints (C) |

QSDP |
MATLAB software for convex quadratic semidefinite programming |

SOCP solvers (second order cone problems, not SDP)

ECOS |
Embedded Conic Solver (Ansi-C, interfaces to Matlab, CVX, Python, library-free) |

SOCP |
software for second order cone programming (C and Matlab) |

LOQO |
interior point method, C, student binaries, executables for major platforms, work for two months w/o license, AMPL interface, Matlab interface |

SQL solvers (semidefinite, quadratic, linear problems, includes SDP, SOCP)

SeDuMi |
Matlab toolbox for solving optimization problems over symmetric cones |

SDPT3-4.0 |
Matlab implementation of infeasible path-following algorithms with Mehrotra type predictor-corrector and two types of search directions. |

MOSEK |
Interior point code for LP, QP, and conic programming. Extended MPS or Matlab input, student license |

CVX |
Matlab package for disciplined convex optimization |

CVXOPT |
Python Software for Convex Optimization |

PICOS |
Python Interface to Conic Optimization Solvers |

SDPpack |
Primal-dual Mehrotra type predictor-corrector scheme, test for degeneracy and other additions, of historical interest |

SDP solvers for discrete optimization problems

BiqCrunch |
A semidefinite branch-and-bound method for solving binary quadratic problems |

SCIP-SDP |
An SDP Plugin for SCIP; solves MISDP |

COPL_SDP |
solves various cut problems, uses dual scaling method(C) |

COPL_DSDP |
mixed integer linear semidefinite problems, enhanced COPL_SDP, MPS-like input (C) |

Max-AO |
solves SDP relaxations of maximum stable set and maximum clique problems, graph input (C) |

KYPD |
solves special KYP SDP problems, needs Yalmip and SeDuMi (Matlab) |

Applications of SDP/SQL/SOCP

TFOCS |
Templates for first order conic solvers (Matlab) |

MVU |
Maximum Variance Unfolding and other machine learning codes (Matlab) |

SFSDP |
MATLAB software for sparse sensor network localization (needs SeDuMi) |

SNLSDP |
MATLAB software for sensor network localization |

Sensor Location |
M and P files for relaxed and full SDP approaches to network sensor location (needs SeDuMi), Matlab |

DSPCA |
Matlab package for sparse principal component analysis |

PICOS |
Python Interface for Conic Optimization Solvers |

YALMIP |
Matlab toolbox for rapid prototyping of optimization problems, supports many solvers; B&B for mixed integer problems |

xLMI |
freely available Matlab LMI solver |

LMITOOL |
LMI parser, part of Scilab |

LMIRANK |
Matlab toolbox for solving rank-constrained LMI problems |

Matrix completions |
Using SDP to solve the PSD and the Euclidean distance matrix completion problems (Matlab) |

FIR toolbox |
Matlab toolbox to optimize FIR filters and similar structures; needs SeDuMi or LOQO or other |

SparsePOP |
Sparse SDP Relaxation of Polynomial Optimization Problems (Matlab) |

GloptiPoly |
Polynomial objective and constraints, integer variables, needs SeDuMi (Matlab, GPL) |

SOSTOOLS |
Matlab toolbox to solve sum of squares polynomial problems; needs SeDuMi and Matlab's symbolic toolbox (GPL) |

Ncpol2sdpa |
Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables, needs SDP solvers, Python paper |

**Geometric programming**

GGPLAB |
Interior point method for GP and generalized GP (Matlab) |

MOSEK |
Interior point method, AMPL, GAMS, Matlab, student license |

COPL_GP / binaries |
Primal-dual interior point method, includes user's guide |

**Robust Optimization**

ROME |
Robust Optimization Made Easy, modeling language and solver, needs CPLEX, or MOSEK, or SDPT3 (Matlab) |

YALMIP |
Extensive tutorial with sample scripts; LP, SDP, SOCP, SoS etc (Matlab) |

**The general nonlinear Problem**

**Using function values only**

The functions f, g, h are not necessarily smooth. Only function values required.

DirectSearch |
for local/global minimization, multi-objective optimization, nonlinear systems, data fitting (Maple) |

LINCOAC# version |
Powell's f77 code for problems with linear inequality constraints (moderate number of variables) |

CONDOR |
parallel, constrained version of Powell's UOBYQA; SIF, AMPL, XML interfaces (C++) |

CONDOR at Github |
serial, unconstrained version of CONDOR (C++) |

COBYLA2 (f77, dble prec)COBYLA2_f90 COBYLA2_C# COBYLA2_C |
The functions depend on few variables (some hundred at most). An SLP method with estimation of gradients by linear interpolation of the individual functions on moving simplices, l_infinity exact penalty function as merit function. Inequality constraints only. M. Powell's paper on Direct Search Methods |

DFO |
derivative free method of Conn, Scheinberg, and Toint |

NOMAD |
LGPL-licensed code to do generalized pattern search for nonlinear and mixed variable optimization (C++) |

NOMADm |
research version of NOMAD (Matlab, part of OPTI Toolbox) |

EI-AL |
hybrid EI-AL method part of the laGP package (R) |

GANSO |
several methods for global&nonsmooth problems (C/C++) |

In the following it is assumed that f, g, h, are differentiable.

**f general, bound constraints only**

BOBYQAC# version |
Powell's bound-constrained optimization by quadratic approximation (f77) |

SDBOX |
derivative-free method (f90 and C) |

fminsearchbnd |
bound-constrained version of fminsearch (Matlab) |

ASA_CG |
bound-constrained version of CG_DESCENT (f77/C) |

tn, C-version |
use tnbc from this package, truncated Newton method using the Lanczos-process, n should be not too large since identification of binding constraints works inefficiently (classical active set method) |

ve08 |
for separable convex f , structured quasi Newton method (Toint-Griewank) |

LBFGS-B, f90, Java, Matlab |
a limited memory quasi Newton (BFGS) method combined with gradient projection for bound constrained problems; directory contains software, drivers and a user's manual |

TRON |
trust region Newton, preconditioned cg, projected search f90-version |

PL2 |
truncated Newton method using the Lanczos process with direct computation of a truncated spectral decomposition, uses a so called three directions method from Heinrich, uses directions of negative curvature. for large dimensional problems. |

LBFGS, LM |
Routines for LBFGS and Levenberg-Marquardt in 6 languages |

LimMem |
Several limited memory f77-routines; also for least squares |

Matlab codes |
Several codes (BFGS, CG), also nonnegativity constraints, applications |

**General linear constraints**

COPL_LC |
f convex, interior point method, needs Hessian |

COPL_LC |
f convex, interior point method, needs Hessian |

PDCO |
f separable convex, primal-dual interior point method (Matlab) |

BlockIP |
optimization package for large convex block-angular problems (C++) |

Most methods for general constraints use an exact nondifferentiable penalty function like the L1-penalty function. The following picture shows this function with weight 1 for h and weights 2 for g_{1} and g_{2} with f(x)=x_{1}+x_{2}, h(x)=x_{1}^2+x_{2}^2-1, g_{1}(x)=x_{1}, g_{2}(x)=x_{2}. It shows some of the intricacies involved in using these functions: not only the nondifferentiability, but also the possible occurrence of infeasible local minimizers. The problem has the two solutions (1,0) with multipliers (0.5,0,1) and (0,1) with multipliers (0.5,1,0). Hence the weights are large enough to make these strict local minima of the penalty function. But three more infeasible minima with the same function value 1 occur at (0,0), (-1,0) and (0,-1).

**General nonlinear constraints, convex problems**

JOptimizer |
Java code for convex optimization |

CVX |
Matlab package for disciplined convex optimization |

CVXOPT |
Python Software for Convex Optimization |

SPG |
Spectral Projected Gradient method, interfaces to AMPL, C/C++, Matlab, Python, Octave, R |

MOSEK |
solves convex, twice differentiable problems, GAMS, Matlab, and AMPL interface, student license |

**General nonlinear constraints, dense linear algebra**

donlp2 |
a SQP/SECQP - method, very fast for regular problems, f77, f90, Ansi-C, exact/numerical/automatic gradients, and ps-files on mathematical background AMPL interface, guide to AMPL version Student binaries of DONLP2 with AMPL for different architectures |

LIONsolver |
reactive search, free for research |

SDPEN |
derivative free sequential penalty method for inequality constrained problems (f90) |

SOLNP |
Matlab-SQP solver, IP solver for QP's, includes manual |

pyFSQP |
python version of old code FSQP |

CONMAX |
uses ODE's to generate search direction followed by Newton to correct back to feasible region, authors claim it is very robust but somewhat slow. |

CONMIN |
old code by Vanderplaats (f90) |

**General nonlinear constraints, sparse linear algebra for high dimensional problems**

Several codes have a CUTEst/SIF interface.

PENLAB |
Open source version of PENNON (Matlab) |

LANCELOT-A |
transforms a general problem into one with nonlinear equality constraints and bound constraints on (some) variables and solves this using a modification of the Hestenes-Powell multiplier method (book: Conn&Gould&Toint: LANCELOT . Springer Series in Comp. Math. 17) AMPL interface |

LANCELOT-B |
part of GALAHAD, updated version, f90 |

WORHP |
SQP solver for very large problems, IP at QP level, exact or approximate second derivatives, various linear algebra options, varius interfaces |

HQP/OMUSES |
motivated by discrete-time optimal control problems, solves general NLP using Powell's or Schittkowski's SQP with Newton-type barrier QP solver, needs Tcl; C++, SIF, or ASCEND input |

SNOPT |
solves large-scale linear and nonlinear problems; especially recommended if some of the constraints are highly nonlinear, or constraints respectively their gradients are costly to evaluate and second derivative information is unavailable or hard to obtain; assumes that the number of "free" variables is modest. AMPL&Matlab interfaces |

MINOS |
also capable of solving nonlinear problems, but not to be recommended for strong nonlinearities, AMPL interface |

KNITRO |
trust region interior point method, efficient for NLPs of all sizes, various interfaces |

IPOPT |
interior point method for large NLP, AMPL&Matlab&Python interfaces (C++) |

IPFILTER |
primal-dual interior point filter method for large NLP, AMPL&SIF&Fortran interfaces (f95) |

LOQO |
interior point method, C, executables for major platforms, work for several months w/o license, AMPL interface, Matlab interface |

PENNON |
Penalty-barrier code for large general NLPs, AMPL interface |

nlpy |
Python package for LP/NLP utilizing Fortran sources and external software |

ALGENCAN |
Augmented Lagrangian type method, interfaces to AMPL, C/C++, Matlab, Python, Octave, R |

SQPlab |
Matlab package for general NLP; needs optimization toolbox or MOSEK |

**Mathematical Problems with Equilibrium Constraints (MPECs)**

IPOPT |
interior point method for large NLP, AMPL interface (C++) |

KNITRO |
trust region interior point method, efficient for NLP's of all sizes, various interfaces |

LOQO |
interior point method, C, student binaries, executables for major platforms, work for two months w/o license, AMPL interface, Matlab interface |

**Minimization of Nonsmooth Functions**

SLQP-GS |
Sequential Linear or Quadratic Programming with Gradient Sampling (Matlab) |

OBOE |
Oracle-Based Optimization Engine for convex problems, uses Proximal-ACCPM interior point method, C++ |

SolvOpt |
Solves nonsmooth unconstrained and constrained problems of moderate dimensions (python). |

NDA |
Four different routines for Lipschitz continuous functions subject to linear constraints and for (small) minimax problems |

**Semi-infinite Programming**

NSIPS |
Three different methods (discretization, interior point, SQP dual), uses author's special AMPL interface (C source and Win-binaries) |

CSIP |
Matlab code for convex semi-infinite programming; AMPL interface |

**Mixed Integer Nonlinear Programming**

DFL |
derivative-free codes for bound and inequality constrained problems (f90) |

Cyber-Infrastructure for MINLP |
Meta site for MINLP |

MINLP World |
forum with links to solvers, problem libraries etc |

BonMin |
hybrid code from COIN-OR, local solver |

Couenne |
Global solver for nonconvex problems |

SCIP |
Global solver for nonconvex problems |

KNITRO |
Local solver based on general NLP code |

MIDACO |
Mixed Integer Distributed Ant Colony Optimization (Matlab, C/C++, Fortran) |

MILANO |
Matlab-based mixed-integer linear and nonlinear solver |

MINLP_BB |
branch&bound and QP/SQP |

Minotaur |
source and Linux/Mac binaries |

LaGO |
B&C, Linux binary, binary variables only, GAMS interface |

BARON |
Global Branch And Reduce Optimization Navigator (avail. from AIMMS, GAMS) |

BNB |
fB&B, Matlab, needs optimization toolbox |

FMINCONSET |
B&B, variables may be restricted to discrete sets, Matlab, needs optimization toolbox |

MINLP |
Matlab code for small number of integer variables |

OPBDPbinaries |
0-1 variables, objective and constraints polynomial (C++) A Davis-Putnam Based Enumeration Algorithm for Linear Pseudo-Boolean Optimization |

**Network Optimization**

**Linear objective function**

MCF |
C, network simplex method |

Net_simplex |
network simplex method, no source (binaries) |

GOBLIN |
Tcl/Tk based for graph and network problems (LGPL, C++ source, binaries) |

PDNET |
interior point method, f77&C |

IPM |
interior point method, f77&C |

MCFClass |
abstract C++ class for single commodity MCF problems incl 5 solvers: RelaxIV, MCFZIB, CS2, MCFCplex, SPTree |

RelaxIV |
MCF solver by Bertsekas&Tseng plus other network and assignment solvers |

Netsoft |
Andrew Goldberg's Network Optimization Library in C |

**Nonlinear objective function**

LSNNO |
f77 code from netlib |

PPRN |
library for various platforms |

PFNRN |
nonlinear constraints, Solaris/Windows binaries |

**Special/constraint Solvers/Languages**

Numberjack |
A Python Constraint Programming platform (interface to many C/C++ solvers) |

Manopt |
Optimization on Riemannian manifolds (Matlab) |

Rational |
Exact solvers for sparse and dense rational linear systems (C, GMP) plus large set of test problems |

GloptLab |
a configurable framework for the rigorous global solution of quadratic constraint satisfaction problems (Matlab) |

ECLiPSe |
Constraint Programming System, source, binaries, public license |

RealPaver |
Interval-based nonlinear constraint solver; source, binaries, documentation (C, BSD license) |

RSOLVER |
Solver for qualified inequality constraints; source, linux binaries, Java GUI, remote access, other constraint solvers |

ICOS |
Interval Constraints Solver, AMPL interface, Linux&Windows-Cygwin binaries |

WSAT(OIP) |
domain independent local search method for linear integer constraints, Linux binary has AMPL/CPLEX interface |

Constraints Archive |
Links to Constraint Programming solvers |

Filtrane |
part of Galahad, nonlinear constraints, filter method, f90 |

MVE |
Finding the largest ellipsoid inscribing a given polytope (GPL, Matlab) |

Miniball |
Finding the smallest enclosing ball of points (GPL, C++) |

Miniball@sourceforge |
Finding the smallest enclosing ball of balls, QPL-licensed, C++ |

**Dynamic Programming**

Open DP |
general dynamic programming software to optimize discrete time processes, with continuous or discrete decisions; random processes (observable or not) allowed |

SDP |
Generalized software for solving stochastic dynamic optimization problems (win executable) |

DP2PN |
Java package for dynamic programming; needs javac |

ACADO |
Toolkit for automatic control and dynamic optimization (C++, Matlab interface) |

CompEcon Tb |
Matlab toolbox for computational economics and finance incl general optimization, dynamic programming, stochastic control |

**Control Problems**

StOpt |
Stochastic Control Library (C++, some python bindings) |

dsoa |
Dynamic System Optimization (C/C++) |

MOOSE |
Model Based Optimal Input Signal Design Toolbox (Matlab) |

ACADO |
Toolkit for control (C++, Matlab interface) |

HPMPC |
Library for High-Performance implementation of solvers for MPC, highly optimized for common architectures; C, Octave interface |

POCP |
Package for Polynomial Optimal Control Problems, uses Gloptipoly or Yalmip (Matlab) |

SQPlab |
Matlab solver for nonlinear optimization and optimal control |

OpenDDPT |
Open Discrete Dynamic Programming Template (C/C++); includes unconstrained optimization package |

LAAS-DO |
Links to various control-related software |

fast_mpc |
implementation of Boyd's method using online optimization (C/Matlab) |

OptControlCentre |
package for the optimization of dynamical systems in energy and chemical engineering |

HIFOO |
A MATLAB package for fixed-order controller design and H-infinity optimization |

GPOPS |
A MATLAB package for multiple phase optimal control; requires SNOPT |

RoMulOC |
Robust Multi-Objective Control toolbox, uses YALMIP (Matlab) |

MPT |
Multi-parametric toolbox for constrained linear and piecewise affine systems (Matlab) |

CompEcon Tb |
Matlab toolbox for computational economics and finance incl general optimization, dynamic programming, stochastic control |

SLICOT |
Control and Systems Library. Very comprehensive. |

MR and LTV Synthesis Tools |
Provides commands for H-Infinity synthesis of discrete LTV systems and multirate sampled LTI systems |

DIRCOL |
Direct collocation method. Optimal ODE control problems with control and state constraints are solved as NLPs with NPSOL or SNOPT |

Control in Java |
A Java Application for the Solution of Optimal Control Problems |

PAREST |
A direct multiple shooting method for the numerical solution of optimal control and parameter estimation problems |

Biomimikry |
Matlab code for Optimization, Control, and Automation |

OCS |
SciLab/Maple based to solve unconstrained ODE control problems |

DAE solvers |
Suite of codes to solve optimal control and related problems |

HQP/OMUSES |
ODE/DAE, automatic differentiation, own format or ASCEND or Simulink input, HQP to solve NLPs (C, C++, f77, Tcl) |

PDECON |
Optimal Control of Ordinary, Algebraic and One-dimensional Partial Differential Equations |

TRICE |
Designed to solve discretized PDE-constrained optimization problems with trust region interior point SQP methods |

**Other collections or problem types**

IPO |
Investigating Polyhedra by Oracles (C++, requires SCIP) |

Optizelle |
Open source software for general NLP problems; multilanguage support |

Compressive Sensing |
software for compressive sensing (mostly Matlab) |

MCQueue |
transient and steady-analysis of discrete-time and continuous-time Markov chains, performance measures or basic queueing models |

SVM software |
Links to Gaussian Processes and SVM software |

IMMOPTIBOX |
Matlab toolbox for Optimization and Data Fitting |

YALMIP |
Matlab toolbox for rapid prototyping of optimization problems, supports 20 solvers |

HYSDEL |
Hybrid Systems Description Language and other downloads |

Modulopt |
Fortran 77 codes for smooth and nonsmooth unconstrained, bound-constrained, and general NLP; test problems |

TANGO |
Collection of Fortran codes for NLP; applications, testproblems. |

CompEcon Tb |
Matlab toolbox for computational economics and finance incl general optimization, dynamic programming, stochastic control |

DAKOTA |
A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis |

OPT++ |
An Object-Oriented Nonlinear Optimization Library |

UFO |
Interactive System for Optimization, very comprehensive; f77 interface for various systems/compilers, library |

TOMLAB |
commercial Matlab optimization package, comprehensive, with interfaces to many state-of-the-art optimization solvers, e.g. CPLEX, FICO-Xpress, MINLP_BB, MIQPBB, filterSQP, PENBMI, PENSDP. It includes SOL software, expensive and non-convex global optimization solvers, approximation methods etc. |

Excel Add-ins |
Rich selection for many OR and optimization problems |

PARAM |
Klaus Schittkowski's software, especially parameter-identification |

KELLEY |
Iterative Methods for Optimization by T. Kelley, codes in Matlab and f77 |

MATLOG |
Facility location and logistics toolbox (Matlab) |

PLT |
production/storage/transport, various solvers as Win binaries |

VRP Web |
comprehensive information/links on VRP |

DistOpt |
Solving large-scale problems through decomposition. Requires Ptolemy, works with various free for research or commercial solvers. Tcl/Tk graphics, C++. |

Cheddar |
GPL-licensed real-time scheduling simulator, source, Win/Linux/Solaris binaries |

FIR toolbox |
Matlab toolbox to optimize FIR filters and similar structures; needs SeDuMi or LOQO or other |

LOLA |
a package for planar location problems (solves continuous and discrete cases) |

StarFLIP |
A reusable iterative optimization library for combinatorial problems with fuzzy constraints (C++) |

MOZART |
Advanced development platform based on Oz. Demos include constraint programming, multi-agent, and concurrent applications. |

Constraints Archive |
More links to Constraint Systems |

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