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Mathematical Optimization Software
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the 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 could be design parameters for a motor, the output could be the power consumption. For another optimization, the inputs could be business choices and the output could be the profit obtained. 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 Eu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation (function)
In mathematics, a transformation, transform, or self-map is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. Partial transformations While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function ''f'': ''A'' → ''B'', where both ''A'' and ''B'' are subsets of some set ''X''. Algebraic structures The set of all transformations on a given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems 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 maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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_(optimization_software), 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. GEK ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boost Software License
Boost is a set of library (computing), libraries for the C++ programming language that provides support for tasks and structures such as linear algebra, pseudorandom number generator, 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 software license, licensed under the #License, Boost Software License, designed to allow Boost to be used with both free software, free and proprietary software projects. Many of Boost's founders are on the ISO/IEC 14882, 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 cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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''. Since then it has been used in a wide range of domains.Nakashima, Yuta, Noboru Bab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...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 promote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, Java). 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 (as of 2023, it supports C++, C#, FreePascal/Delphi, VB.NET, Python, and Java) * 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 for the Civil Service, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scilab
Scilab is a free and open-source, cross-platform numerical computational package and a high-level, numerically oriented programming language. It can be used for signal processing, statistical analysis, image enhancement, fluid dynamics simulations, numerical optimization, and modeling, simulation of explicit and implicit dynamical systems and (if the corresponding toolbox is installed) symbolic manipulations. Scilab is one of the two major open-source alternatives to MATLAB, the other one being GNU Octave. Scilab puts less emphasis on syntactic compatibility with MATLAB than Octave does, but it is similar enough that some authors suggest that it is easy to transfer skills between the two systems. Introduction Scilab is a high-level, numerically oriented programming language. The language provides an interpreted programming environment, with matrices as the main data type. By using matrix-based computation, dynamic typing, and automatic memory management, many numerical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
