Semi-Infinite Programming and Applications to Minimax Problems

A minimisation problem with infinitely many constraints – semi-infinite programming problem (SIP) is considered. The problem is solved using a two stage procedure that searches for global maximum violation of the constraints. A version of the algorithm that searches for any violation of constraints is also considered, and the performance of the two algorithm is compared. An application to solving minimax problem (with and without coupled constraints) is given and a comparison with the algorithm for continuous minimax of Rustem and Howe (2001) is included. Finally, we consider an application to chemical engineering problems.