THE SEMISMOOTH APPROACH FOR SEMI-INFINITE PROGRAMMING WITHOUT STRICT COMPLEMENTARITY

Stein O., Tezel A.

SIAM JOURNAL ON OPTIMIZATION, vol.20, no.2, pp.1052-1072, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1137/080719765
  • Journal Name: SIAM JOURNAL ON OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1052-1072
  • Keywords: generalized semi-infinite optimization, semismooth Newton method, nonlinear complementarity problem function, Clarke subdifferential regularity, Reduction Ansatz, NEWTON METHODS, ALGORITHM, EQUATIONS
  • Hacettepe University Affiliated: No

Abstract

As a complement of our recent article [O. Stein and A. Tezel, J. Global Optim., 41 (2008), pp. 245-266], we study convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems. The semismooth Newton method is applied to a semismooth reformulation of the upper and lower level Karush-Kuhn-Tucker conditions by nonlinear complementarity problem functions into a semismooth system of equations. In the present paper we assume strict complementary slackness neither in the upper nor in the lower level. The auxiliary functions of the locally reduced problem then are not necessarily twice continuously differentiable. Still, we can show that a standard regularity condition for quadratic convergence of the semismooth Newton method holds under a natural assumption for semi-infinite programs.