Journal of Optimization Theory and Applications

, Volume 146, Issue 2, pp 419–443 | Cite as

Feasible Method for Generalized Semi-Infinite Programming

Article

Abstract

In this paper, we analyze the outer approximation property of the algorithm for generalized semi-infinite programming from Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). A simple bound on the regularization error is found and used to formulate a feasible numerical method for generalized semi-infinite programming with convex lower-level problems. That is, all iterates of the numerical method are feasible points of the original optimization problem. The new method has the same computational cost as the original algorithm from Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). We also discuss the merits of this approach for the adaptive convexification algorithm, a feasible point method for standard semi-infinite programming from Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007).

Keywords

Semi-infinite programming Interior-point method Mathematical program with equilibrium constraints Bilevel programming Design centering 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Fraunhofer Institut für Techno- und WirtschaftsmathematikKaiserslauternGermany

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