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Generalized semi-infinite programming : ウィキペディア英語版 | 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: : : :: where : : : : In the special case that the set : is nonempty for all GSIP can be cast as bilevel programs (Multilevel programming).
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