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Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of the best solution from some set of available alternatives, [1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process.
Xpress was originally developed by Dash Optimization, and was acquired by FICO in 2008. [3] Its initial authors were Bob Daniel and Robert Ashford. The first version of Xpress could only solve LPs; support for MIPs was added in 1986. Being released in 1983, Xpress was the first commercial LP and MIP solver running on PCs. [4]
FICO Xpress – solver for linear and quadratic programming with continuous or integer variables (MIP). FortMP – linear and quadratic programming. FortSP – stochastic programming. GAMS – General Algebraic Modeling System. Gurobi Optimizer – solver for linear and quadratic programming with continuous or integer variables (MIP).
AMPL Optimization LLC was founded by the inventors of AMPL, Robert Fourer, David Gay, and Brian Kernighan. The new company took over the development and support of the AMPL modeling language from Lucent Technologies, Inc. 2005 AMPL Modeling Language Google group opened [11] 2008 Kestrel: An AMPL Interface to the NEOS Server introduced 2012
free/commercial: A dual-licensed C++/C#/Java/Python numerical analysis library with parallel SOCP solver. AMPL: commercial: An algebraic modeling language with SOCP support Artelys Knitro: commercial: CPLEX: commercial: FICO Xpress: commercial: Gurobi Optimizer: commercial: MATLAB: commercial: The coneprog function solves SOCP problems [12 ...
The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization.GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems.
The IBM ILOG CPLEX Optimizer solves integer programming problems, very large [3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).
nl is a file format for presenting and archiving mathematical programming problems. [1] Initially, this format has been invented for connecting solvers to AMPL. [2] It has also been adopted by other systems such as COIN-OR (as one of the input formats), FortSP (for interacting with external solvers), and Coopr (as one of its output formats).