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AMPL is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing . 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.
The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations. The system is available for use on various computer platforms. Models are portable from one platform to another.
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in Fortran and C and is released under the EPL. IPOPT implements a primal-dual interior point method, and uses line searches based on Filter methods. IPOPT can be called from various modeling environments and C.
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 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.
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation. One particular advantage of some algebraic modeling languages like AIMMS, AMPL, GAMS, Gekko, MathProg, Mosel, and OPL is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it.
Ellis Lane Johnson is the Professor Emeritus and the Coca-Cola Chaired Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology in Atlanta, Georgia.
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.
AIMMS is a prescriptive analytics software company with offices in the Netherlands, United States and Singapore.
Jon Lee is an American mathematician and operations researcher, the G. Lawton and Louise G. Johnson Professor of Engineering at the University of Michigan. He is known for his research in nonlinear discrete optimization and combinatorial optimization.
George Lann Nemhauser is an American operations researcher, the A. Russell Chandler III Chair and Institute Professor of Industrial and Systems Engineering at the Georgia Institute of Technology and the former president of the Operations Research Society of America.
MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities.
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.
JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language. JuMP is used by companies, government agencies, academic institutions, software projects, and individuals to formulate and submit optimization problems to third‑party solvers. JuMP has been specifically applied to problems in the field of operations research.
Deterministic global optimization is a branch of numerical 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 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, 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.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
The NEOS Server is an Internet-based client-server application that provides free access to a library of optimization solvers. Its library of solvers includes more than 60 commercial, free and open source solvers, which can be applied to mathematical optimization problems of more than 12 different types, including linear programming, integer programming and nonlinear optimization.
Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other. Robust algorithms and modeling language interfaces have been developed for a large variety of mathematical programming problems such as linear programs (LPs), nonlinear programs (NPs), Mixed Integer Programs (MIPs), mixed complementarity programs (MCPs) and others. Researchers are constantly updating the types of problems and algorithms that they wish to use to model in specific domain applications.
ANTIGONE, is a deterministic global optimization solver for general Mixed-Integer Nonlinear Programs (MINLP).
Octeract Engine is a proprietary massively parallel deterministic global optimization solver for general Mixed-Integer Nonlinear Programs (MINLP), and the current world record holder in MINLP performance.
References
- ↑ "A comparison of complete global optimization solvers" (PDF). Archived from the original (PDF) on 2022-08-08. Retrieved 2022-09-21.
- ↑ "BARON on the NEOS Server". Archived from the original on 2013-06-29. Retrieved 2016-01-26.
- ↑ "ICS Prize / Prizes / ICS / Community / IOL Home - INFORMS.org". October 20, 2010. Archived from the original on 2010-10-20.
- ↑ "Mathematical Optimization Society". May 21, 2011. Archived from the original on 2011-05-21.
- ↑ "Professor Nikolaos V. Sahinidis". February 22, 2023. Archived from the original on 2023-02-03. Retrieved 2023-02-22.
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