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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 Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Fourer
Robert Fourer (born September 2, 1950) is a scientist working in the area of operations research and management science. He is currently President of AMPL Optimization, Inc and is Professor Emeritus of Industrial Engineering and Management Sciences at Northwestern University. Robert Fourer is recognized as being the designer of the popular modeling language for mathematical programming called AMPL. Together with David M. Gay and Brian Kernighan he was awarded 1993 ORSA/CSTS Prize by the Computer Science Technical Section of the Operations Research Society of America, for writings on the design of mathematical programming systems and the AMPL modeling language. Robert Fourer was also awarded Guggenheim Fellowship for Natural Sciences in 2002. He was elected to the 2004 class of Fellows of the Institute for Operations Research and the Management Sciences. Prior to the invention of AMPL, a series of articles by Fourer extended the Simplex algorithm to allow for the objective to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Definition and discussion Let ''n'', ''m'', and ''p'' be positive integers. Let ''X'' be a subset of ''Rn'' (usually a box-constrained one), let ''f'', ''gi'', and ''hj'' be real-valued functions on ''X'' for each ''i'' in and each ''j'' in , with at least one of ''f'', ''gi'', and ''hj'' being nonlinear. A nonlinear programming problem is an optimization problem of the form : \begin \text & f(x) \\ \text ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sol (format)
sol is a file format for representing solutions of mathematical programming problems. It is often used in conjunction with the nl format to return solutions from the solvers. Initially this format has been invented for connecting solvers to AMPL 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 ... but then it has been adopted by other systems such as FortSP for interacting with external solvers. The sol format is low-level and is designed for compactness not for readability. It has both binary and textual representation. Many solvers such as CPLEX and MOSEK can produce files in this format either directly or through special driver programs. The AMPL Solver Library (ASL) which allows among other things to read and write the sol files is open-source. It is used in many solvers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parsing
Parsing, syntax analysis, or syntactic analysis is a process of analyzing a String (computer science), string of Symbol (formal), symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar by breaking it into parts. The term ''parsing'' comes from Latin ''pars'' (''orationis''), meaning Part of speech, part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional Sentence (linguistics), sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams. It usually emphasizes the importance of grammatical divisions such as subject (grammar), subject and predicate (grammar), predicate. Within computational linguistics the term is used to refer to the formal analysis by a computer of a sentence or other string of words into its constituents, resulting in a par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug tracking system, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, GitHub, Inc. has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. GitHub reported having over 100 million developers and more than 420 million Repository (version control), repositories, including at least 28 million public repositories. It is the world's largest source code host Over five billion developer contributions were made to more than 500 million open source projects in 2024. About Founding The development of the GitHub platform began on October 19, 2005. The site was launched in April 2008 by Tom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Netlib
Netlib is a repository of software for scientific computing maintained by AT&T, Bell Laboratories, the University of Tennessee and Oak Ridge National Laboratory. Netlib comprises many separate programs and libraries. Most of the code is written in C and Fortran, with some programs in other languages. History The project began with email distribution on UUCP, ARPANET and CSNET in the 1980s. The code base of Netlib was written at a time when computer software was not yet considered merchandise. Therefore, no license terms or terms of use are stated for many programs. Before the Berne Convention Implementation Act of 1988 (and the earlier Copyright Act of 1976) works without an explicit copyright notice were public-domain software. Also, most of the Netlib code is work of US government employees and therefore in the public domain. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Programming
Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological backtracking and constraint propagation, but may use customized code like a problem-specific branching heuristic. Constraint programming takes its root from and can be expressed in the form of constraint logic programming, which embeds constraints into a logic program. This variant of logic programming is due ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementarity Theory
A complementarity problem is a type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a function of two vector variables subject to certain requirements (constraints) which include: that the inner product of the two vectors must equal zero, i.e. they are orthogonal. In particular for finite-dimensional real vector spaces this means that, if one has vectors ''X'' and ''Y'' with all ''nonnegative'' components (''x''''i'' ≥ 0 and ''y''''i'' ≥ 0 for all i: in the first quadrant if 2-dimensional, in the first octant if 3-dimensional), then for each pair of components ''x''''i'' and ''y''''i'' one of the pair must be zero, hence the name ''complementarity''. e.g. ''X'' = (1, 0) and ''Y'' = (0, 2) are complementary, but ''X'' = (1, 1) and ''Y'' = (2, 0) are not. A complementarity problem is a special case of a variational inequality. History Complementarity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Form
In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called '' vectors'') over a field ''K'' (the elements of which are called '' scalars''). In other words, a bilinear form is a function that is linear in each argument separately: * and * and The dot product on \R^n is an example of a bilinear form which is also an inner product. An example of a bilinear form that is not an inner product would be the four-vector product. The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms. When is the field of complex numbers , one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument. Coordinate representation Let be an - dimensional vector space with basis . The matrix ''A'', defined by is called the ''matrix of the bilinear form'' on the basis . If the matrix represents a ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semidefinite Programming
Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDPs are used in the context of linear matrix inequalities. SDPs are in fact a special case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as SDPs, and via hierarchies of SDPs the solutions of polynomial optimization problems can be approximated. Semidefinite programming ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Optimization
Global optimization is a branch of operations research, applied mathematics, and numerical analysis that attempts to find the global minimum or maximum of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function g(x) is equivalent to the minimization of the function f(x):=(-1)\cdot g(x). Given a possibly nonlinear and non-convex continuous function f:\Omega\subset\mathbb^n\to\mathbb with the global minimum f^* and the set of all global minimizers X^* in \Omega, the standard minimization problem can be given as :\min_f(x), that is, finding f^* and a global minimizer in X^*; where \Omega is a (not necessarily convex) compact set defined by inequalities g_i(x)\geqslant0, i=1,\ldots,r. Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding ''local'' minima or maxima. Finding an arbitrary local m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second-order Cone Programming
A second-order cone program (SOCP) is a convex optimization problem of the form :minimize \ f^T x \ :subject to ::\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m ::Fx = g \ where the problem parameters are f \in \mathbb^n, \ A_i \in \mathbb^, \ b_i \in \mathbb^, \ c_i \in \mathbb^n, \ d_i \in \mathbb, \ F \in \mathbb^, and g \in \mathbb^p. x\in\mathbb^n is the optimization variable. \lVert x \rVert_2 is the Euclidean norm and ^T indicates transpose In linear algebra, the transpose of a Matrix (mathematics), matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other .... The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (A x + b, c^T x + d) to lie in the second-order cone in \mathbb^. SOCPs can be solved by interior point methods and in general, can be solved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
