We list here the above mentioned tools only. Others may be useful and/or even necessary, like preprocessors for systems of linear inequalities and equations, e.g. for eliminating fixed variables, redundant equalities and inequalities and similar tasks. There is no separate public domain software tool for these tasks. Some of the modeling systems mentioned below, however, include such options.
While it is frequently necessary or desirable to replace gradients by numerical differentiation, a tool that became available more recently is that of automatic differentiation. NLP programs which have both options include DONLP2 and FSQP (see under programs for general nonlinear programming). A comparison of the various differentiation techniques is given in Griewank's paper.
The following are links to some general automatic differentiation software: These codes take a subprogram for computing a function as input and automatically generate a subprogram for computing the gradient and/or the Hessian as output.
| Tapenade | Source-to-source f77 (C, and most of f95); websubmission or local installation as JAR archive |
| ADiGator | Source transformation Matlab package, may be called repeatedly |
| ADOL-C | A. Griewank's packages for programs in C/C++, forward and reverse mode |
| ADiMAT | web-based automatic differentiation in Matlab, forward mode |
| INTLAB | automatic differentiation in Matlab, forward modes |
| CppAD | Operator overloading package for C++ |
| CasADi | symbolic framework for algorithmic differentiation and numerical optimization (C++, Python) |
| Revolve | checkpointing for reverse mode |
| more AD tools |
Modeling languages allow you to formulate a linear or nonlinear programming problem in mathematical terms in a way near your original problem and automatically generate an evaluation code appropriate for a corresponding solver. Different solvers need different interfaces, hence not all codes come with interfaces for such modeling languages. The following example shows a typical problem in mathematical terms, coded in C , coded in the modeling language AMPL, and finally coded in SIF ALKYLATION . SIF means standard input format and has been developed by Conn, Gould and Toint in connection with their LANCELOT project. It is an extension of the old linear programming MPS format. If one has coded a problem in SIF, then the SIF evaluation tools allow computation of exact first and second order derivatives. SIF is fully documented in the book A.R. Conn, N.I.M. Gould, Ph. L. Toint: "LANCELOT A Fortran Package for Large-Scale Nonlinear Optimization", Springer publisher, 1992, ISBN 3-540-55470-X.Here comes a list of some modeling languages/systems:
| AMPL | The AMPL modeling language is a commercial product, but a lot is available freely here. |
| GAMS | commercial modeling system with many solvers and related services |
| ADMB | software package for the development of nonlinear statistical models, uses AUTODIF (C++, binaries, Windows, Linux, MacOS) |
| AIMMS | commercial modeling platform, interactive graphical display, educational package |
| CasADi | symbolic framework for algorithmic differentiation and numerical optimization (C++, Python) |
| GEKKO | object-oriented python library for mixed-integer and differential-algebraic equations, requires local APMonitor suite |
| Pyomo | Flexible modeling of optimization problems in Python (formerly COIN-OR Coopr) |
| JuMP | Modeling Language for linear, integer, and quadratic programming, part of Julia, benchmarks here |
| StructJuMP | Parallel algebraic modeling framework for block structured optimization models in Julia |
| CMPL | modeling language and interface to several LP/MILP solvers |
| plam | A free MILP modeling environment using lp_solve as MILP solver and SWI-Prolog |
| PuLP | Python-based LP modeler, calls GLPK, Coin-CLP/CBC, CPLEX, GUROBI, XPRESS |
| SDPSL | Semidefinite Programming Specification Language, SAGE interface (C++) |
| FLOPC++ | C++ class library for algebraic modelling of linear optimization problems (LP/MIP); uses COIN OSI interface. |
| ZIMPL | GPL-licensed LP/MILP modelling language, produces lp/MPS formats (C) |
| ASCEND | An extensive GPL-licensed modeling system (source, binaries, docs). |
| IPAT-S | Extensive LGPL-licensed scenario scripting language, GUI, Win executables, source; includes lp_solve. |
| Solver-o-matic | Decision tree to choose solver for nonsmooth problems from list of opensource codes |
| PIPAL | Penalty-Sequential Quadratic Programming with Infeasibility Detection for general NLP (Matlab, AMPL input) |
| Interactive Modules | Java-based demos of basic optimization methods; also least squares and nonlinear equations |
| perPlex | Tool to verify the feasibility, optimality, and integrality of a linear programming basis (C, GPL) |
| MProbe | Analysis tool for Nonlinear Programs (AMPL, GAMS, MPS, Win student version) |
| MINOS(IIS) | Software Tool for Analyzing Infeasible Linear Programs (Win student version) |
