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AMPL Programming Language
AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (e.g. large-scale optimization and scheduling-type problems). It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial software, including CBC, CPLEX, FortMP, MOSEK, MINOS, IPOPT, SNOPT, KNITRO, and LGO. Problems are passed to solvers as nl files. AMPL is used by more than 100 corporate clients, and by government agencies and academic institutions. One advantage of AMPL is the similarity of its syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization. Many modern solvers available on the NEOS Server (formerly hosted at the Argonne National Laboratory, currently hosted at the University of Wisconsin, Madison) accept AMPL ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open Source Software
Free and open-source software (FOSS) is software available under a Software license, license that grants users the right to use, modify, and distribute the software modified or not to everyone free of charge. FOSS is an inclusive umbrella term encompassing free software and open-source software. The rights guaranteed by FOSS originate from the "Four Essential Freedoms" of ''The Free Software Definition'' and the criteria of ''The Open Source Definition''. All FOSS can have publicly available source code, but not all source-available software is FOSS. FOSS is the opposite of proprietary software, which is licensed restrictively or has undisclosed source code. The historical precursor to FOSS was the hobbyist and academic public domain software ecosystem of the 1960s to 1980s. Free and open-source operating systems such as Linux distributions and descendants of BSD are widely used, powering millions of server (computing), servers, desktop computer, desktops, smartphones, and othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KNITRO
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems. KNITRO – (the original solver name) short for "Nonlinear Interior point Trust Region Optimization" (the "K" is silent) – was co-created by Richard Waltz, Jorge Nocedal, Todd Plantenga and Rich Byrd. It was first introduced in 2001, as a derivative of academic research at Northwestern University. Subsequently, it was developed by Ziena Optimization LLC, which has been bought by Frech Artelys. Optimization problems must be presented to Knitro in mathematical form, and should provide a way of computing function derivatives using sparse matrices (Knitro can compute derivatives approximation but in most cases providing the exact derivatives is beneficial). An often easier approach is to develop the optimization problem in an algebraic modeling language. The modeling environment computes function derivatives, and Knitro is called as a "solver" from within the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SNOPT
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available. It employs a sparse sequential quadratic programming (SQP) algorithm with limited-memory quasi-Newton approximations to the Hessian of the Lagrangian. It is especially effective for nonlinear problems with functions and gradients that are expensive to evaluate. The functions should be smooth but need not be convex. SNOPT is used in several trajectory optimization software packages, including Copernicus, AeroSpace Trajectory Optimization and Software ( ASTOS), General Mission Analysis Tool, and Optimal Trajectories by Implicit Simulation (OTIS). It is also available in the Astrogator module of Systems Tool Kit. SNOPT is supported in the AIMMS, AMPL AMPL (A Mathematical Programming Language) is an al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IPOPT
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in C++ (after migrating from Fortran and C) and is released under the EPL (formerly CPL). IPOPT implements a primal-dual interior point method, and uses line searches based on Filter methods ( Fletcher and Leyffer). IPOPT can be called from various modeling environments: C, C++, Fortran, Java, R, Python, and others. IPOPT is part of the COIN-OR project. IPOPT is designed to exploit 1st derivative ( gradient) and 2nd derivative ( Hessian) information if provided (usually via automatic differentiation routines in modeling environments such as AMPL). If no Hessians are provided, IPOPT will approximate them using a quasi-Newton methods, specifically a BFGS update. IPOPT was originally developed by Ph.D. studenAndreas Wächterand ProfLorenz T. Bieglerof the Department of Chemical Engineering at Carneg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MINOS (optimization Software)
__NOTOC__ MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS (Modular In-core Nonlinear Optimization System) may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities. MINOS was first developed by Bruce Murtagh and Michael Saunders, mostly at the Systems Optimization Laboratory in the Department of Operations Research at Stanford University. In 1985, Saunders was awarded the inaugural Orchard-Hays prize by the Mathematical Programming Society (now the Mathematical Optimization Society) for his work on MINOS. Despite being one of the first general-purpose constrained optimization solvers to emerge, the package remains heavily used. MINOS is supported in the AIMMS, AMPL, APMonitor, GAMS, and TOMLAB modeling systems. In addition, it remains one of the top-used solver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MOSEK
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer science. The emphasis in MOSEK is on solving large-scale sparse problems linear and conic optimization problems. In particular, MOSEK solves conic quadratic (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming) problems. A special feature of the solver, is its interior-point optimizer, based on the so-called homogeneous model. This implies that MOSEK can reliably detect a primal and/or dual infeasible status as documented in several published papers. In addition to the interior-point optimizer MOSEK includes: * Primal and dual simplex optimizer for linear problems. * Mixed-integer optimizer for linear, quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FortMP
FortMP is a software package for solving large-scale optimization problems. It solves linear programming problems, quadratic programming problems and mixed integer programming problems (both linear and quadratic). Its robustness has been explored and published in the Mathematical Programming journal. FortMP is available as a standalone executable that accepts input in MPS format and as a library with interfaces in C and Fortran. It is also supported in the AMPL modeling system. The main algorithms implemented in FortMP are the primal and dual simplex algorithms using sparse matrices. These are supplemented for large problems and quadratic programming problems by interior point methods. Mixed integer programming problems are solved using branch and bound Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPLEX
IBM ILOG CPLEX Optimization Studio (often informally referred to simply as CPLEX) is an optimization software package. History The CPLEX Optimizer was named after the simplex method implemented in the C programming language. However, today it also supports other types of mathematical optimization and offers interfaces other than C. It was originally developed by Robert E. Bixby and sold commercially in 1988 by CPLEX Optimization Inc. This was acquired by ILOG in 1997 and ILOG was subsequently acquired by IBM in January 2009. CPLEX continues to be actively developed by IBM. Features The IBM ILOG CPLEX Optimizer solves integer programming problems, very large 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). The CPLEX Optimizer has a modelin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commercial Software
Commercial software, or, seldom, payware, is a computer software that is produced for sale or that serves commercial purposes. Commercial software can be proprietary software or free and open-source software. Background and challenge While software creation by programming is a time and labor-intensive process, comparable to the creation of physical goods, the reproduction, duplication and sharing of software as digital goods is in comparison disproportionately easy. No special machines or expensive additional resources are required, unlike almost all physical goods and products. Once the software is created it can be copied in infinite numbers, for almost zero cost, by anyone. This made commercialization of software for the mass market in the beginning of the computing era impossible. Unlike hardware, it was not seen as trade-able and commercialize-able good. Software was plainly shared for free (hacker culture) or distributed bundled with sold hardware, as part of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open-source Software
Open-source software (OSS) is Software, computer software that is released under a Open-source license, license in which the copyright holder grants users the rights to use, study, change, and Software distribution, distribute the software and its source code to anyone and for any purpose. Open-source software may be developed in a collaborative, public manner. Open-source software is a prominent example of open collaboration, meaning any capable user is able to online collaboration, participate online in development, making the number of possible contributors indefinite. The ability to examine the code facilitates public trust in the software. Open-source software development can bring in diverse perspectives beyond those of a single company. A 2024 estimate of the value of open-source software to firms is $8.8 trillion, as firms would need to spend 3.5 times the amount they currently do without the use of open source software. Open-source code can be used for studying and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solver
A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a Library (computing), software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type. Solver types Types of problems with existing dedicated solvers include: * Linear equation, Linear and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm. * System of linear equations, Systems of linear equations. * Nonlinear systems. * Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers. * Linear and non-linear Optimization (mathematics), optimisation problems * Systems of ordinary differential equations * Systems of differential algebraic equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
