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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.
IBM ILOG CPLEX Optimization Studio is an optimization software package. In 2004, the work on CPLEX earned the first INFORMS Impact Prize.
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.
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available.
CUTEr is an open source testing environment for optimization and linear algebra solvers. CUTEr provides a collection of test problems along with a set of tools to help developers design, compare, and improve new and existing test problem solvers.
The Galahad library is a thread-safe library of packages for the solution of mathematical optimization problems. The areas covered by the library are unconstrained and bound-constrained optimization, quadratic programming, nonlinear programming, systems of nonlinear equations and inequalities, and non-linear least squares problems. The library is mostly written in the Fortran 90 programming language.
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
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, 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.
Advanced process monitor (APMonitor) is a modeling language for differential algebraic (DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
nl is a file format for presenting and archiving mathematical programming problems. Initially this format has been invented for connecting solvers to AMPL. It has also been adopted by other systems such as COIN-OR, FortSP, and Coopr.
The Zuse Institute Berlin is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany.
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.
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise and other inaccuracies, and produces estimates of unknown variables or parameters. Unlike deterministic approaches, MHE requires an iterative approach that relies on linear programming or nonlinear programming solvers to find a solution.
Optimization Toolbox is an optimization software package developed by MathWorks. It is an add-on product to MATLAB, and provides a library of solvers that can be used from the MATLAB environment. The toolbox was first released for MATLAB in 1990.
The FICO Xpress optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts. Xpress includes a general purpose non-linear solver, Xpress NonLinear, including a successive linear programming algorithm, and Artelys Knitro.
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.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
The GEKKO Python package solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers. 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.
Octeract Engine is a proprietary massively parallel deterministic global optimization solver for general Mixed-Integer Nonlinear Programs (MINLP). It uses MPI as a means of accelerating solution times. It is notable for its parallelism and for being the only commercial optimization solver that is free to use.
References
- ↑ WOpatent 2012005740,Lawson, K. W., Hedengren, J. D., Smith, L. C.,"Method for Controlling Bubble Formation in Polymerization Reactors",published 2012-01-12
- ↑ Spivey, B. (2010). "Constrained Nonlinear Estimation for Industrial Process Fouling". Industrial & Engineering Chemistry Research. 49 (17): 7824–7831. doi:10.1021/ie9018116.
- ↑ Nielsen, Isak (2012). Modeling and Control of Friction Stir Welding in 5 cm thick Copper Canisters (M.Sc. thesis). Linköping University.
- ↑ Brower, D. (2012). "Fiber Optic Monitoring of Subsea Equipment" (PDF). OMAE 2012 Proceedings, Rio de Janeiro, Brazil.
- ↑ Brower, D. (2013). "Advanced Deepwater Monitoring System" (PDF). OMAE 2013 Proceedings, Nantes, France.
- ↑ Abbott, C. (2012). "New Capabilities for Large-Scale Models in Computational Biology" (PDF). AIChE Annual Meeting Proceedings, Pittsburgh, PA.
- ↑ Spivey, B. (2010). "Dynamic Modeling of Reliability Constraints in Solid Oxide Fuel Cells and Implications for Advanced Control" (PDF). AIChE Annual Meeting Proceedings, Salt Lake City, Utah.
- ↑ Jacobsen, L. (2013). "Model Predictive Control with a Rigorous Model of a Solid Oxide Fuel Cell" (PDF). American Control Conference (ACC), Washington, DC.
- ↑ Sun, L. (2013). "Optimal Trajectory Generation using Model Predictive Control for Aerially Towed Cable Systems" (PDF). Journal of Guidance, Control, and Dynamics.
- ↑ Hedengren, J. (2012). "APOPT: MINLP Solver for Differential Algebraic Systems with Benchmark Testing" (PDF). INFORMS Annual Meeting.