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Deterministic Global Optimization
Deterministic global optimization is a branch of mathematical optimization which focuses on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one, within some predefined tolerance. The term "deterministic global optimization" typically refers to complete or rigorous (see below) optimization methods. Rigorous methods converge to the global optimum in finite time. Deterministic global optimization methods are typically used when locating the global solution is a necessity (i.e. when the only naturally occurring state described by a mathematical model is the global minimum of an optimization problem), when it is extremely difficult to find a feasible solution, or simply when the user desires to locate the best possible solution to a problem. Overview Neumaier classified global optimization methods in four categories, depending on their degree of rigour with which they approach the optimum, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
BARON
Baron is a rank of nobility or title of honour, often Hereditary title, hereditary, in various European countries, either current or historical. The female equivalent is baroness. Typically, the title denotes an aristocrat who ranks higher than a lord or knight, but lower than a viscount or count. Often, barons hold their fief – their lands and income – directly from the monarch. Barons are less often the vassals of other nobles. In many kingdoms, they were entitled to wear a smaller form of a crown called a ''coronet''. The term originates from the Late Latin, Latin term , via Old French. The use of the title ''baron'' came to England via the Norman Conquest of 1066, then the Normans brought the title to Scotland and Southern Italy. It later spread to Scandinavian and Slavic lands. Etymology The word '':wikt:baron, baron'' comes from the Old French , from a Late Latin "man; servant, soldier, mercenary" (so used in Salic law; Alemannic law has in the same sense). The sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SCIP (optimization Software)
The Zuse Institute Berlin (abbreviated ZIB, or ''Konrad-Zuse-Zentrum für Informationstechnik Berlin'') is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany. The ZIB was founded by law as a statutory establishment and as a non-university research institute of the State of Berlin in 1984. In close interdisciplinary cooperation with the Berlin universities and scientific institutions Zuse Institute implements research and development in the field of information technology with a particular focus on application-oriented algorithmic mathematics and practical computer science. ZIB also provides high-performance computer capacity as an accompanying service as part of the ''Network of high performance computers in Northern Germany'' (Norddeutscher Verbund von Hoch- und Höchstleistungsrechnern (HLRN)). Konrad Zuse, born in Berlin in 1910, is the namesake of the ZIB. SCIP (optimization software) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octeract Engine
Octeract Engine is a proprietary massively parallel deterministic global optimization solver for general Mixed-Integer Nonlinear Programs (MINLP). The solver is designed to work in parallel on a distributed environment. It is optimized for succeeding in synthetic benchmark sets. The latest world records were set in April 2023, when it became the first optimization solver to ever solve all problems in the benchmark, with a world record setting unscaled shifted geometric mean of 36.8. History Octeract Engine was developed by Nikos Kazazakis and Gabriel Lau. The first public beta version of Octeract Engine was released in August 2019, and it came out of beta in August 2020. Performance On 23 July 2022 it ranked first on the single thread Mittelmann MINLPLIB benchmark. This lead has been maintained for all releases of Octeract Engine hence. As of August 2022 it is the first and only solver to solve the largest open transmission switching problems in the industry standard MINLPLIB ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LINDO
LINDO (Linear, Interactive, and Discrete Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization. LINGO is a mathematical modeling language used as part of LINDO. Today, LINDO solvers are part of LINDO API (Application Programming Interface) a set of software libraries that can be called from different programming languages to create custom mathematical optimization applications. It is designed to solve optimization problems that arise in areas of business, industry, research, and government. The LINDO package includes sample applications related to product distribution, ingredient blending, production, personnel scheduling, inventory management. LINDO also creates "What's''Best!''" which is an add-in for linear, integer and nonlinear optimization. First released for Lotus 1-2-3 and later also for Microsoft Excel. Features * LINDO provides routines to formulate, solve, query, and m ... [...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] |
Julia (programming Language)
Julia is a high-level programming language, high-level, general-purpose programming language, general-purpose dynamic programming language, dynamic programming language, designed to be fast and productive, for e.g. data science, artificial intelligence, machine learning, modeling and simulation, most commonly used for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, a default just-in-time compilation, just-in-time (JIT) compiler (with support for ahead-of-time compilation) and an tracing garbage collection, efficient (multi-threaded) garbage collection implementation. Notably Julia does not support classes with encapsulated methods and instead it relies on structs with generic methods/functions not tied to them. By default, Julia is run similarly to scripting languages, using its runtime, and allows for read–eval–print loop, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sven Leyffer
Sven Leyffer is an American computational mathematician specializing in nonlinear optimization. He is a Senior Computational Mathematician in the Laboratory for Applied Mathematics, Numerical Software, and Statistics at Argonne National Laboratory. Education Leyffer received a Vordiplom in Pure and Applied Mathematics from the University of Hamburg in 1989. Leyffer obtained his Ph.D. in 1994 from the University of Dundee under doctoral advisor Roger Fletcher. His dissertation was ''Deterministic Methods in Mixed Integer Nonlinear Programming''. Recognition In 2006, Leyffer was awarded, alongside Roger Fletcher and Philippe L. Toint, the Lagrange Prize from the Mathematical Programming Society (MPS) and the Society for Industrial and Applied Mathematics (SIAM). In 2009, Leyffer was named a Fellow of the Society for Industrial and Applied Mathematics (SIAM) for ''contributions to large-scale nonlinear optimization.'' Service From 2017 to 2021, Leyffer was Editor-in-Chief of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Couenne
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open-source library for solving global optimization problems, also termed mixed integer nonlinear optimization problems. A global optimization problem requires to minimize a function, called objective function, subject to a set of constraints. Both the objective function and the constraints might be nonlinear and nonconvex. For solving these problems, Couenne uses a reformulation procedure and provides a linear programming approximation of any nonconvex optimization problem.P. Belotti, J. Lee, L. Liberti, F. Margot, & A. Wächter (2009), Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods & Software, 24(4-5), 597-634. Couenne is an implementation of a branch-and-bound where every subproblem is solved by constructing a linear programming relaxation to obtain a lower bound. Branching may occur at both continuous and integer variables, which is necessary in global optimizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modeling Language
A modeling language is any artificial language that can be used to express data, information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure of a programming language. Overview A modeling language can be graphical or textual. * ''Graphical'' modeling languages use a diagramming technique, diagram technique with named symbols that represent concepts and lines that connect the symbols and represent relationships and various other graphical notation to represent constraints. * ''Textual'' modeling languages may use standardized keywords accompanied by parameters or natural language terms and phrases to make computer-interpretable expressions. An example of a graphical modeling language and a corresponding textual modeling language is EXPRESS (data modeling language), EXPRESS. Not all modeling languages are executable, and for those that are, the use of them does ... [...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 (e.g. 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, MOSEK, 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) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AIMMS
AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States, and Singapore. It has two main product offerings that provide modeling and optimization capabilities across a variety of industries. The AIMMS Prescriptive Analytics Platform allows advanced users to develop optimization-based applications and deploy them to business users. AIMMS SC Navigator, launched in 2017, is built on the AIMMS Prescriptive Analytics Platform and provides configurable Apps for supply chain teams. SC Navigator provides supply chain analytics to non-advanced users. History AIMMS B.V. was founded in 1989 by mathematician Johannes Bisschop under the name of Paragon Decision Technology. His vision was to make optimization more approachable by building models rather than programming. In Bisschop's view, modeling was able to build the bridge between the people who had problems and the people helping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
