A Branch-and-Bound Approach for Solving a Class of Generalized Semi-infinite Programming Problems

Authors:
E. Levitin;R. Tichatschke
Affiliations:
Institute of System Analysis, Russian Academy of Science, 117312 Moscow, Russia/;Department of Mathematics, University of Trier, 54286 Trier, Germany (e-mail: Email: tichat@uni-trier.de)
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

A nonconvex generalized semi-infinite programming problem isconsidered, involving parametric max-functions in both the objective and theconstraints. For a fixed vector of parameters, the values of theseparametric max-functions are given as optimal values of convex quadraticprogramming problems. Assuming that for each parameter the parametricquadratic problems satisfy the strong duality relation, conditions aredescribed ensuring the uniform boundedness of the optimal sets of the dualproblems w.r.t. the parameter. Finally a branch-and-bound approach issuggested transforming the problem of finding an approximate global minimumof the original nonconvex optimization problem into the solution of a finitenumber of convex problems.