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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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. It is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Energy Modelling Initiative
The Open Energy Modelling Initiative (openmod) is a grassroots community of energy system modellers from universities and research institutes across Europe and elsewhere. The initiative promotes the use of open-source software and open data in energy system modelling for research and policy advice. The Open Energy Modelling Initiative documents a variety of open-source energy models and addresses practical and conceptual issues regarding their development and application. The initiative runs an email list, an internet forum, and a wiki and hosts occasional academic workshops. A statement of aims is available. Context The application of open-source development to energy modelling dates back to around 2003. This section provides some background for the growing interest in open methods. Growth in open energy modelling Just two active open energy modelling projects were cited in a 2011 paper: OSeMOSYS and TEMOA. Balmorel was also public at that time, having been ma ... [...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] |
Simplex Algorithm
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial ''cones'', and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function. History George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator. During 1946 his colleague challenged him to mechanize the planning process to distract him from taking another job. Dantzig formulated the problem as linear inequalities inspired by the work of Wassily Leontief, however, at that t ... [...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 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 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. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Optimization Software
Given a transformation between input and output values, described by a Function (mathematics), mathematical function ''f'', Mathematical optimization, 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 (mathematics), function ''f'' : ''A'' \to R from some Set (mathematics), 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' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JuMP
Jumping is a form of locomotion or movement in which an organism or non-living (e.g., robotic) mechanical system propels itself through the air along a ballistic trajectory. Jump or Jumping also may refer to: Places * Jump, Kentucky or Jump Station, an unincorporated community in Floyd County * Jump, Ohio, a community in Hardin County * Jump, South Yorkshire, a village in Barnsley, England Science and engineering * Jump discontinuity, a change in value of a mathematical function * Jump, a step in a statistical jump process * Jump, a step in a jump diffusion process * Hydraulic jump, a phenomenon in fluid dynamics Computing * Jump instruction, used to alter the control flow of a program * JumpDrive, a brand of, or a generic term for, USB flash drives * Turing jump, an operator in recursion theory Media * ''Jump'' (magazine line), a line of manga magazines ** Weekly Shōnen Jump, the best-selling magazine of the line, often referred to as just ''Jump'' * Jump (musical), a Kore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. Scope As opposed to continuous optimization, some or all of the variables used in a discrete mathematical program are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers. Branches Three notable branches of discrete optimization are:. * combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures * integer programming * constraint programming These branches are all closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.g. shortest path) or constraint programs, any constraint program can be formulated as an integer program and vice versa, and constraint and integer programs can often be given a combinatorial interpretation. See also *Diophantine equation In mathematics, a Diophantine equation is an equation, typically a pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SciPy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering. SciPy is also a family of conferences for users and developers of these tools: SciPy (in the United States), EuroSciPy (in Europe) and SciPy.in (in India). Enthought originated the SciPy conference in the United States and continues to sponsor many of the international conferences as well as host the SciPy website. The SciPy library is currently distributed under the BSD license, and its development is sponsored and supported by an open community of developers. It is also supported by NumFOCUS, a community foundation for supporting reproducible and accessible science. Components The SciPy package is at the core of Python's scientific computing capabilit ... [...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 at finding 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, 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 simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Application Software
Application may refer to: Mathematics and computing * Application software, computer software designed to help the user to perform specific tasks ** Application layer, an abstraction layer that specifies protocols and interface methods used in a communications network * Function application, in mathematics and computer science Processes and documents * Application for employment, a form or forms that an individual seeking employment must fill out * College application, the process by which prospective students apply for entry into a college or university * Patent application, a document filed at a patent office to support the grant of a patent Other uses * Application (virtue), a characteristic encapsulated in diligence * Topical application, the spreading or putting of medication to body surfaces See also * * Apply {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cholesky Decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. Statement The Cholesky decomposition of a Hermitian positive-definite matrix A, is a decomposition of the form : \mathbf = \mathbf^*, where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. The converse holds trivially: if A can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
