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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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. As part of the GNU Project, it is free software under the terms of the GNU General Public License. History The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Full development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 7.1.0 was released on Apr 6, 2022. The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations. Development history Developments In addi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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HiGHS Optimization Solver
HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, JavaScript, Fortran, and C#. It has no external dependencies. Although generally single-threaded, some solver components can utilize multi-core architectures. HiGHS is designed to solve large-scale models and exploits problem sparsity. Its performance relative to commercial and other open-source software is reviewed periodically using industry-standard benchmarks. The term HiGHS may also refer to both the underlying project and the small team leading the software development. History HiGHS is based on solvers written by PhD students from the Optimization and Operational Research Group in the School of Mathematics at the University of Edinburgh. Its origins can be traced back to late 2016, when Ivet Galabova ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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GLPK
The GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. The package is part of the GNU Project and is released under the GNU General Public License. Problems can be modeled in the language GNU MathProg (previously known as GMPL) which shares many parts of the syntax with AMPL and solved with standalone solver GLPSOL. GLPK can also be used as a C library. GLPK uses the revised simplex method and the primal-dual interior point method for non-integer problems and the branch-and-bound algorithm together with Gomory's mixed integer cuts for (mixed) integer problems. GLPK is supported in the free edition of the OptimJ modeling system An independent project provides a Java-based interface to GLPK (via JNI). This allows Java applications to call out to GLPK in a relativel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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MIT License
The MIT License is a permissive free software license originating at the Massachusetts Institute of Technology (MIT) in the late 1980s. As a permissive license, it puts only very limited restriction on reuse and has, therefore, high license compatibility. Unlike copyleft software licenses, the MIT License also permits reuse within proprietary software, provided that all copies of the software or its substantial portions include a copy of the terms of the MIT License and also a copyright notice. , the MIT License was the most popular software license found in one analysis, continuing from reports in 2015 that the MIT License was the most popular software license on GitHub. Notable projects that use the MIT License include the X Window System, Ruby on Rails, Nim, Node.js, Lua, and jQuery. Notable companies using the MIT License include Microsoft ( .NET), Google ( Angular), and Meta ( React). License terms The MIT License has the identifier MIT in the SPDX License List. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Gekko (optimization Software)
The GEKKO Python package solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS). Modes of operation include machine learning, data reconciliation, real-time optimization, dynamic simulation, and nonlinear model predictive control. In addition, the package solves Linear programming (LP), Quadratic programming (QP), Quadratically constrained quadratic program (QCQP), Nonlinear programming (NLP), Mixed integer programming (MIP), and Mixed integer linear programming (MILP). GEKKO is available in Python and installed with pip from PyPI of the Python Software Foundation. pip install gekko GEKKO works on all platforms and with Python 2.7 and 3+. By default, the problem is sent to a public server where the solution is computed and returned to Python. There are Windows, MacOS, Linux, and ARM (Raspberry Pi) processor options to solve without an Internet connection. GEKKO is an extension of the APM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Boost Software License
Boost is a set of libraries for the C++ programming language that provides support for tasks and structures such as linear algebra, pseudorandom number generation, multithreading, image processing, regular expressions, and unit testing. It contains 164 individual libraries (as of version 1.76). All of the Boost libraries are licensed under the Boost Software License, designed to allow Boost to be used with both free and proprietary software projects. Many of Boost's founders are on the C++ standards committee, and several Boost libraries have been accepted for incorporation into the C++ Technical Report 1, the C++11 standard (e.g. smart pointers, thread, regex, random, ratio, tuple) and the C++17 standard (e.g. filesystem, any, optional, variant, string_view). The Boost community emerged around 1998, when the first version of the standard was released. It has grown continuously since then and now plays a big role in the standardization of C++. Even though there is no formal r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dlib
Dlib is a general purpose cross-platform software library written in the programming language C++. Its design is heavily influenced by ideas from design by contract and component-based software engineering. Thus it is, first and foremost, a set of independent software components. It is open-source software released under a Boost Software License. Since development began in 2002, Dlib has grown to include a wide variety of tools. As of 2016, it contains software components for dealing with networking, threads, graphical user interfaces, data structures, linear algebra, machine learning, image processing, data mining, XML and text parsing, numerical optimization, Bayesian networks, and many other tasks. In recent years, much of the development has been focused on creating a broad set of statistical machine learning tools and in 2009 Dlib was published in the ''Journal of Machine Learning Research The ''Journal of Machine Learning Research'' is a peer-reviewed open access scientif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Eclipse Public License
The Eclipse Public License (EPL) is a free and open source software license most notably used for the Eclipse IDE and other projects by the Eclipse Foundation. It replaces the Common Public License (CPL) and removes certain terms relating to litigations related to patents.In section 7, this sentence is in CPL 1.0, but not EPL 1.0: "If Recipient institutes patent litigation against a Contributor with respect to a patent applicable to software (including a cross-claim or counterclaim in a lawsuit), then any patent licenses granted by that Contributor to such Recipient under this Agreement shall terminate as of the date such litigation is filed." The Eclipse Public License is designed to be a business-friendly free software license, and features weaker copyleft provisions than licenses such as the GNU General Public License (GPL). The receiver of EPL-licensed programs can use, modify, copy and distribute the work and modified versions, in some cases being obligated to release th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 promo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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ALGLIB
ALGLIB is a cross-platform open source numerical analysis and data processing library. It can be used from several programming languages ( C++, C#, VB.NET, Python, Delphi). ALGLIB started in 1999 and has a long history of steady development with roughly 1-3 releases per year. It is used by several open source projects, commercial libraries, and applications (e.g. TOL project, Math.NET Numerics, SpaceClaim). Features Distinctive features of the library are: * Support for several programming languages with identical APIs (, it supports C++, C#, FreePascal/Delphi, VB.NET and Python) * Self-contained code with no mandatory external dependencies and easy installation * Portability (it was tested under x86/x86-64/ARM, Windows and Linux) * Two independent backends (pure C# implementation, native C implementation) with automatically generated APIs (C++, C#, ...) * Same functionality of commercial and GPL versions, with enhancements for speed and parallelism provided in the commercial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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CeCILL
CeCILL (from CEA CNRS INRIA Logiciel Libre) is a free software license adapted to both international and French legal matters, in the spirit of and retaining compatibility with the GNU General Public License (GPL). It was jointly developed by a number of French agencies: the ''Commissariat à l'Énergie Atomique'' (Atomic Energy Commission), the ''Centre national de la recherche scientifique'' (National Centre for Scientific Research) and the ''Institut national de recherche en informatique et en automatique'' (National Institute for Research in Computer Science and Control). It was announced on 5 July 2004 in a joint press communication of the CEA, CNRS and INRIA. It has gained support of the main French Linux User Group and the Minister of Public Function, and was considered for adoption at the European level before the European Union Public Licence was created. Terms The CeCILL grants users the right to copy, modify, and distribute the licensed software freely. It defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |