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Linear semi-infinite programming: a guide tour: Miguel A. Goberna
Linear semi-infinite programming (LSIP) deals with linear optimization problems in which either the dimension of the decision space or the number of constraints (but not both) is in.nite. This work describes the state-of-the-art in LSIP, identifying the most active research .elds, the main trends in applications, and the more challenging open problems. After an introduction to the basic concepts and results in LSIP, where the properties of the constraint systems play a crucial role, we overview the main numerical approaches in LSIP, underlying recent contributions. We survey LSIP models arising in mathe- matical economics, game theory, probability and statistics as well as outstanding real applications of LSIP in semi-infinite programming, electronics, communications and control problems, in which numerical experiments are reported. Finally, we review recent contributions in the more active theoretical research field, parametric LSIP, including stability and sensitivity results providing qualitative and quantitative information, respectively, about the impact on the primal and dual values and other objects of small changes in the data.
Mathematics Subject Classi.cation (2000): Primary: 90C34, 90C05; Secondary: 15A39, 49K40. Key words : semi-infinite optimization, linear inequality systems.