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Parametric programming : ウィキペディア英語版 | Parametric programming
Parametric programming is a type of mathematical optimization, where the optimization problem is solved as a function of one or multiple parameters.〔Tomas Gal. Postoptimal analyses, parametric programming, and related topics: Degeneracy, multicriteria decision making, redundancy. Berlin : W. de Gruyter, 1995.〕 Developed in parallel to sensitivity analysis, its earliest mention can be found in a thesis from 1952.〔T Gal, H.J. Greenberg Advances in Sensitivity Analysis and Parametric Programming. Springer, 1997.〕 Since then, there have been considerable developments for the cases of multiple parameters, presence of integer variables as well as nonlinearities. In particular the connection between parametric programming and model predictive control established in 2000 has contributed to an increased interest in the topic.〔Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N. (2000) The explicit solution of model predictive control via multiparametric quadratic programming. Proceedings of the American Control, vol. 2, 872–876.〕〔Bemporad, Alberto; Morari, Manfred; Dua, Vivek; Pistikopoulos, Efstratios N. (2002) The explicit linear quadratic regulator for constrained systems. Automatica, 38 (1), 3–20.〕 == Notation == In general, the following optimization problem is considered : where is the optimization variable, are the parameters, is the objective function and denote the constraints. Note that the space is generally referred to as parameter space.
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