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AMPL (textbook Cover)
AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., 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, 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 input. Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMPL (textbook Cover)
AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., 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, 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 input. Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Modeling Language
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems). One particular advantage of some algebraic modeling languages like AIMMS, AMPL, GAMS, Gekko, MathProg, Mosel, and OPL is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it. An AML does not solve those problems directly; instead, it calls appropriate external algorithms to obtain a solution. These algorithms are called solvers and can handle certain kind of mathematical probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nl (format)
nl is a file format for presenting and archiving mathematical programming problems. Initially, this format has been invented for connecting solvers to AMPL. 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). The nl format supports a wide range of problem types, among them: * Linear programming * Quadratic programming * Nonlinear programming * Mixed-integer programming * Mixed-integer quadratic programming with or without convex quadratic constraints * Mixed-integer nonlinear programming * Second-order cone programming * Global optimization * Semidefinite programming problems with bilinear matrix inequalities * Complementarity problems (MPECs) in discrete or continuous variables * Constraint programming The nl format is low-level and is designed for compactness, not for readability. It has both binary and textual representation. Most commercial and a ... [...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 Richard Byrd. It was first introduced in 2001, as a derivative of academic research at Northwestern University (through Ziena Optimization LLC), and has since been continually improved by developers at 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 en ... [...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, APMonitor, General Algebraic Modeling System (GAMS), and TOM ... [...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 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 and C. IPOPT is part of the COIN-OR project. IPOPT is designed to exploit 1st and 2nd derivative ( Hessians) 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 Carnegie Mellon University. Their work was recognized with thINFORMS Computing Society Prizein 2009. Arvind ... [...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 solvers on ... [...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 an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumera ... [...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. In 2004, the work on CPLEX earned the first INFORMS Impact Prize. History The CPLEX Optimizer was named for the simplex method as implemented in the C programming language, although 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 from 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 ... [...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 a 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 service t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open-source Software
Open-source software (OSS) is computer software that is released under a license in which the copyright holder grants users the rights to use, study, change, and 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 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 2008 report by the Standish Group stated that adoption of open-source software models has resulted in savings of about $60 billion per year for consumers. Open source code can be used for studying and allows capable end users to adapt software to their personal needs in a similar way user scripts an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
