See also: Plato: Decision Tree for Optimization Software

The NEOS Optimization Server is an online optimization server. The optimization solvers represent the state-of-the-art in optimization software. Optimization problems are solved automatically with minimal input from the user. Users only need a definition of the optimization problem; all additional information required by the optimization solver is determined automatically.

TAO: Toolkit for Advanced Optimization

Arnold Neumaier's overview

Michael Trick's Operations Research Page

SeDuMi SeDuMi is software for optimization over symmetric cones.

SDPT3 a MATLAB software for semidefinite-quadratic-linear programming

SDPpack is a system for semidefinite programming (SDP) to mixed semidefinite-quadratic-linear programs (SQLP), i.e. linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant.

The OpsResearch Links Page is a nice collection of links for optimization and simulation.

CCLP-LAND (Composite Concave Linear Programming) is an extension of linear programming allowing a broad class non-linear objective functions. However, the constraints must remain linear.

SolvOpt is a collection of the M-files for use with Matlab, FORTRAN and C source codes. SolvOpt (Solver for local optimization problems) is concerned with minimization or maximization of nonlinear, possibly non-smooth objective functions and solution of nonlinear minimization problems taking into account constraints by the method of exact penalization. SolvOpt is a freeware and comes with no warranty.

John Chinneck's MProbe is a software tool for analyzing mathematical programming models. It has special capabilities for analyzing nonlinear functions to discern their shapes in a region of interest (i.e. whether the function is linear or almost linear, convex or almost convex, concave or almost concave, or concave and convex). Knowledge of function shape is crucial when developing nonlinear optimization models, or when selecting the nonlinear solver for a nonlinear optimization problem. Determining function shape is difficult for nonlinear functions having more than two variables. MProbe is specifically designed to operate on nonlinear functions having many variables. MProbe also estimates the shape of a nonlinearly constrained region (convex? nonconvex?), the objective function effect (global optimum? local optimum only?), and the effectiveness of the constraints.

Automatic Diff NLP is an automatic differentiation version of Peter Spellucci's NLP package DONLP2. It uses the TAMC utility of Ralf Giering.

AMPL (Commercial package) is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, in discrete or continuous variables. Developed at Bell Laboratories, AMPL lets you use common notation and familiar concepts to formulate optimization models and examine solutions, while the computer manages communication with an appropriate solver. AMPL's flexibility and convenience render it ideal for rapid prototyping and model development, while its speed and control options make it an especially efficient choice for repeated production runs.

MINOPT (Commercial package) is a comprehensive, powerful, and flexible package for the solution of various types of optimization problems. It features both an ADVANCED MODELING LANGUAGE for the clear and concise representation of complex mathematical models as well as a ROBUST ALGORITHMIC FRAMEWORK for the efficient solution of wide variety of mathematical programming problems.

APPSPACK is the implementation of an asynchronous and fault tolerant parallel pattern search method for unconstrained or bound constrained optimization. Pattern search uses only function values for optimization, so it can be applied to a wide variety of problems, such as engineering optimization design problems characterized by a small number of variables and by expensive objective function evaluations (typically complex simulations that take minutes or hours to run). Parallelism is achieved by dividing the search directions and corresponding function evaluations among the different processors. The asynchronicity is due to the fact that the search along each direction continues without waiting for searches along other directions to finish, in contrast to the standard parallel pattern search method. Further, APPS is also fault tolerant so it is not hindered by node failures. APPSPACK uses either PVM or MPI for parallel communications, and it can also be run serially.

SBmethod is a C++ code for large scale eigenvalue optimization. SBmethod implements the spectral bundle method for minimizing the maximum eigenvalue of an affine matrix function (real and symmetric). The code is intended for large scale problems. It supports sign constraints on the design variables and allows to exploit structural properties of the matrices such as sparsity and low rank structure.

Galahad is a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. GALAHAD includes two packages for nonconvex quadratic programming (one being interior-point based, the other is of the active/working set variety), a quadratic programming preprocessing package, an updated version of LANCELOT, and a number of other subsidiary optimization-related tools. Full PostScript and PDF documentation is included, as are installation scripts for a variety of Unix-like platforms.

OPT++ 2.0 is an object-oriented package for nonlinear optimization. The new version includes support for general linear and nonlinear constraints, a new parallel optimization method, and a new nonlinear interior point method. Other capabilities include parallel direct search, nonlinear conjugate gradient, quasi-Newton and full Newton methods. OPT++ has been ported to various platforms including IX86 Linux, Sun, SGI, and DEC. A complete set of documentation has also been added with descriptions of the major classes and extensive sample problems. The new release of OPT++ is under the GNU Lesser GPL license.

Optimization, Linear and Non-Linear Programming: References

Bertsekas, Dimitri, 1999, Nonlinear Programming, Athena Scientific. Excellent.

Chvatal, Vasek, 1983, Linear Programming, W.H. Freeman. A current classic for graduate and upper level undergraduate courses. For better or worse, it's light on mathematics.

Robert J. Vanderbei Linear Programming: Foundations and Extensions Kluwer Academic Publishers. This book is an introductory graduate textbook on linear programming although upper-level graduate students and researchers will find plenty of material here that cannot be found in other books. It has also been used successfully to teach undergraduates majoring in Operations Research. Balanced treatment of the simplex method and interior-point methods. Efficient source code (in C) for all the algorithms presented in the text, available from: Vanderbei

Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, McGraw-Hill (1996).

Tam\'as Terlaky (Ed.) Interior Point Methods of Mathematical Programming, Kluwer Academic Publishers, 1996. This book primarily intends to give an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time we try to give a quick overview of the impact, of the extensions of IPMs to smooth nonlinear optimization and to give an impression of the potentials of IPMs in solving difficult practical problems.

Practical Methods of Optimization, R. Fletcher, John Wiley, 1987. Excellent practical text on non-linear programming.

J.E. Dennis Jr. and R.B. Schnabel, Numerical Methods for Nonlinear Optimization and Nonlinear Equations, Siam, 1983

Gill, Murray and Wright, 2 volume set on Nonlinear Programming.

K.G.Murty, 1988, Linear Complementarity, Linear and Nonlinear Programming, Heldermann Verlag.

Bazraa and Shetty. Nonlinear Programming, theory and algorithms,

Luenberger, Linear and Nonlinear Programming

Yair Censor and Stavros A. Zenios, 1997, Parallel Optimization: Theory, Algorithms, and Applications, Oxford University Press.

C. Roos, T. Terlaky and J.-Ph. Vial. 1997. Theory and Algorithms for Linear Optimization: An Interior Point Approach John Wiley, Chichester

Stephen J. Wright, 1997, Primal-Dual Interior-Point Methods, SIAM. In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software.

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