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MOSEK
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, 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, in particular the interior-point optimizer for linear, conic quadratic (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming), which the software is considerably efficient solving. 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-int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mosek Logo
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, 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, in particular the interior-point optimizer for linear, conic quadratic (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming), which the software is considerably efficient solving. 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-int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization Software
Given a transformation between input and output values, described by a mathematical function ''f'', optimization deals with generating and selecting a best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function, and recording the best output values found during the process. Many real-world problems can be modeled in this way. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit. An optimization problem, in this case a minimization problem, can be represented in the following way :''Given:'' a function ''f'' : ''A'' \to R from some set ''A'' to the real numbers :''Search for:'' an element ''x''0 in ''A'' such that ''f''(''x''0) ≤ ''f''(''x'') for all ''x'' in ''A''. In continuous optimization, ''A'' is some subset of the Euclidean space R''n'', often spec ... [...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] |
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. 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 efficiently than semidefinite programming (SDP) problems. Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. Applications in quantitative finance include p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semidefinite Programming
Semidefinite programming (SDP) is a subfield of convex optimization 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 has been use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denmark
) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Danish Realm, Kingdom of Denmark , established_title = History of Denmark#Middle ages, Consolidation , established_date = 8th century , established_title2 = Christianization , established_date2 = 965 , established_title3 = , established_date3 = 5 June 1849 , established_title4 = Faroese home rule , established_date4 = 24 March 1948 , established_title5 = European Economic Community, EEC 1973 enlargement of the European Communities, accession , established_date5 = 1 January 1973 , established_title6 = Greenlandic home rule , established_date6 = 1 May 1979 , official_languages = Danish language, Danish , languages_type = Regional languages , languages_sub = yes , languages = German language, GermanGerman is recognised as a protected minority language in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan area has 2,057,142 people. Copenhagen is on the islands of Zealand and Amager, separated from Malmö, Sweden, by the Øresund strait. The Øresund Bridge connects the two cities by rail and road. Originally a Viking fishing village established in the 10th century in the vicinity of what is now Gammel Strand, Copenhagen became the capital of Denmark in the early 15th century. Beginning in the 17th century, it consolidated its position as a regional centre of power with its institutions, defences, and armed forces. During the Renaissance the city served as the de facto capital of the Kalmar Union, being the seat of monarchy, governing the majority of the present day Nordic region in a personal union with Sweden and Norway ruled by the Danis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CVX (optimization Software)
CVX may refer to: *Chevron Corporation (NYSE stock ticker: CVX) *Charlevoix Municipal Airport (FAA airport code CVX) * Critical Viscosity of Xenon experiment * Christian Life Community * Chinese VX (EA-6043), an organophosphate nerve agent of the V-series *CVX-class aircraft carrier, South Korean aircraft carrier class in development See also * ''Gerald R. Ford''-class aircraft carrier, codenamed CVNX in development * CVX Live, a YouTuber convention *CV (other) CV, Cv, or cv may refer to: *Curriculum vitae, a summary of academic and professional history and achievements CV, Cv, or cv may also refer to: Arts, entertainment, and media * CV (novel), ''CV'' (novel), a novel by Damon Knight * Character voi ... * CV10 (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in ''Mathematica''. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. __TOC__ Notebook interface Wolfram Mathematica (called ''Mathematica'' by some of its users) is split into two parts: the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end. The origin ... [...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] |
