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MPS (format)
MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. Overview The format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the commercial LP solvers. Essentially all commercial LP solvers accept this format, and it is also accepted by the open-source COIN-OR system. Other software may require a customized reader routine in order to read MPS files. However, with the acceptance of algebraic modeling languages MPS usage has declined. For example, according to the NEOS server statistics in January 2011 less than 1% of submissions were in MPS form compared to 59.4% of AMPL and 29.7% of GAMS submissions. MPS is column-oriented (as opposed to entering the model as equations), and all model components (variables, rows, etc.) receive names. MPS is an old format, so it is set up for punch cards: Fields start in column 2, 5, 15, 25, 40 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Integer Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where this function has the smallest (or largest) value if such a point exists. Linear programs are problems that can be expressed in canonical form as : \begin & \text && \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of technical limitations of computer systems at the time it was invented, ASCII has just 128 code points, of which only 95 are , which severely limited its scope. All modern computer systems instead use Unicode, which has millions of code points, but the first 128 of these are the same as the ASCII set. The Internet Assigned Numbers Authority (IANA) prefers the name US-ASCII for this character encoding. ASCII is one of the List of IEEE milestones, IEEE milestones. Overview ASCII was developed from telegraph code. Its first commercial use was as a seven-bit teleprinter code promoted by Bell data services. Work on the ASCII standard began in May 1961, with the first meeting of the American Standards Association's (ASA) (now the American Nat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
COIN-OR
Computational Infrastructure for Operations Research (COIN-OR), is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature (e.g., a research journal) provides the operations research (OR) community with a peer-review process and an archive. Papers in operations research journals on mathematical theory often contain supporting numerical results from computational studies. The software implementations, models, and data used to produce the numerical results are typically not published. The status quo impeded researchers needing to reproduce computational results, make fair comparisons, and extend the state of the art. The success of Linux, Apache, and other projects popularized the open-source model of software development and distribution. A group at IBM Research proposed open source as an analogous yet viable means to ''publish'' software, models, and data. COIN-OR was conceived as an initiative to promot ... [...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] |
Argonne National Laboratory
Argonne National Laboratory is a science and engineering research United States Department of Energy National Labs, national laboratory operated by University of Chicago, UChicago Argonne LLC for the United States Department of Energy. The facility is located in Lemont, Illinois, outside of Chicago, and is the largest national laboratory by size and scope in the Midwest. Argonne had its beginnings in the Metallurgical Laboratory of the University of Chicago, formed in part to carry out Enrico Fermi's work on nuclear reactors for the Manhattan Project during World War II. After the war, it was designated as the first national laboratory in the United States on July 1, 1946. In the post-war era the lab focused primarily on non-weapon related nuclear physics, designing and building the first power-producing nuclear reactors, helping design the reactors used by the United States' nuclear navy, and a wide variety of similar projects. In 1994, the lab's nuclear mission ended, and today ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMPL
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] |
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] |
Stochastic Programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions. This framework contrasts with deterministic optimization, in which all problem parameters are assumed to be known exactly. The goal of stochastic programming is to find a decision which both optimizes some criteria chosen by the decision maker, and appropriately accounts for the uncertainty of the problem parameters. Because many real-world decisions involve uncertainty, stochastic programming has found applications in a broad range of areas ranging from finance to transportation to energy optimization. Two-stage problems The basic idea of two-stage stochastic programming is that (optimal) decisions should be based on data available at the time the decisions are made and cannot depend on futur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
