A BRANCH-AND-BOUND APPROACH FOR SOLVING A CLASS OF GENERALIZED SEMIINFINITE PROGRAMMING-PROBLEMS

A nonconvex generalized semi-infinite programming problem is considere d, involving parametric max-functions in both the objective and the co nstraints. For a fixed vector of parameters, the values of these param etric max-functions are given as optimal values of convex quadratic pr ogramming problems. Assuming that for each parameter the parametric qu adratic problems satisfy the strong duality relation, conditions are d escribed ensuring the uniform boundedness of the optimal sets of the d ual problems w.r.t. the parameter. Finally a branch-and-bound approach is suggested transforming the problem of finding an approximate globa l minimum of the original nonconvex optimization problem into the solu tion of a finite number of convex problems.