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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
