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Generalized Semi-infinite Programming
In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.O. Stein and G. Still, On generalized semi-infinite optimization and bilevel optimization', European J. Oper. Res., 142 (2002), pp. 444-462 Mathematical formulation of the problem The problem can be stated simply as: : \min\limits_\;\; f(x) : \mbox\ :: g(x,y) \le 0, \;\; \forall y \in Y(x) where :f: R^n \to R :g: R^n \times R^m \to R :X \subseteq R^n :Y \subseteq R^m. In the special case that the set :Y(x) is nonempty for all x \in X GSIP can be cast as bilevel programs ( Multilevel programming). Methods for solving the problem Examples See also * optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-Infinite Programming
In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints. In the former case the constraints are typically parameterized. * * M. A. Goberna and M. A. López, ''Linear Semi-Infinite Optimization'', Wiley, 1998. * Mathematical formulation of the problem The problem can be stated simply as: : \min_\;\; f(x) : \text :: g(x,y) \le 0, \;\; \forall y \in Y where :f: R^n \to R :g: R^n \times R^m \to R :X \subseteq R^n :Y \subseteq R^m. SIP can be seen as a special case of bilevel programs in which the lower-level variables do not participate in the objective function. Methods for solving the problem In the meantime, see external links below for a complete tutorial. Examples In the meantime, see external links below for a complete tutorial. See also * Optimization Mathematical optimization (alternative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilevel Programming
Multilevel or multi-level may refer to: * A hierarchy, a system where items are arranged in an "above-below" relation. * A system that is composed of several layers. * Bombardier MultiLevel Coach The Bombardier MultiLevel Coach is a bi-level passenger rail car manufactured by Bombardier for use on commuter rail lines. The first units were delivered in 2006 and deliveries (in various orders) continued to 2014. Overview There are 643 o ..., a passenger rail car by Bombardier. See also * * {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
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 maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
