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Semi-infinite Programming

  • Osman Güler
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 258)

Abstract

Semi-infinite programs are constrained optimization problems in which the number of decision variables is finite, but the number of constraints is infinite. In this chapter, we treat a class semi-infinite programming problems in which the constraints are indexed by a compact set. We will demonstrate the usefulness of such problems by casting several important optimization problems in this form and then using semi-infinite programming techniques to solve them. Historically, Fritz John [148] initiated semi-infinite programming precisely to deduce important results about two such geometric problems: the problems of covering a compact body in \( \mathbb{R}^n \) by the minimum-volume disk and the minimum-volume ellipsoid. In the same landmark paper, he derived what are now called Fritz John optimality conditions for this class of semi-infinite programs.

Keywords

Convex Body Nonexpansive Function Lipschitz Continuous Function Volume Ellipsoid Fritz John Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of MarylandBaltimoreUSA

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