Generalized semi-infinite programming: Numerical aspects

Abstract

Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretization and an exchange method are derived under fairly general assumptions. The question under which conditions GSIP represents a convex problem is answered