The semismooth approach for semi-infinite programming under the Reduction Ansatz

Stein O., Tezel A.

JOURNAL OF GLOBAL OPTIMIZATION, vol.41, no.2, pp.245-266, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1007/s10898-007-9228-z
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.245-266
  • Keywords: generalized semi-infinite optimization, semismooth Newton method, NCP function, CD-regularity, reduction Ansatz, NEWTON METHODS, EQUATIONS
  • Middle East Technical University Affiliated: Yes


We study convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems where, using NCP functions, the upper and lower level Karush-Kuhn-Tucker conditions of the optimization problem are reformulated as a semismooth system of equations. Nonsmoothness is caused by a possible violation of strict complementarity slackness. We show that the standard regularity condition for convergence of the semismooth Newton method is satisfied under natural assumptions for semi-infinite programs. In fact, under the Reduction Ansatz in the lower level and strong stability in the reduced upper level problem this regularity condition is satisfied. In particular, we do not have to assume strict complementary slackness in the upper level. Numerical examples from, among others, design centering and robust optimization illustrate the performance of the method.