APPLICATION OF A PRIMAL-DUAL INTERIOR POINT ALGORITHM USING EXACT SECOND ORDER INFORMATION WITH A NOVEL NON-MONOTONE LINE SEARCH METHOD TO GENERALLY CONSTRAINED MINIMAX OPTIMISATION PROBLEMS

This work presents the application of a primal-dual interior point method tominimax optimisation problems. The algorithm differs significantly fromprevious approaches as it involves a novel non-monotone line search procedure,which is based on the use of standard penalty methods as the merit functionused for line search. The crucial novel concept is the discretisation of thepenalty parameter used over a finite range of orders of magnitude and theprovision of a memory list for each such order. An implementation within alogarithmic barrier algorithm for bounds handling is presented with capabilitiesfor large scale application. Case studies presented demonstrate the capabilitiesof the proposed methodology, which relies on the reformulation of minimaxmodels into standard nonlinear optimisation models. Some previously reportedcase studies from the open literature have been solved, and with significantlybetter optimal solutions identified. We believe that the nature of the nonmonotoneline search scheme allows the search procedure to escape from localminima, hence the encouraging results obtained.