J. Schwientek/H. Berthold (Fraunhofer ITWM, Kaiserslautern)

Semi-infinite programming has become a powerful modeling tool in (continuous) optimization tasks and is increasingly used in many practical problems from various fields recently. This is mainly due to the enormous further development of computer technology and numerical methods, which now make such problems tractable on standard PCs within reasonable time. The talk is divided into two parts. Firstly, we give a short introduction to (general) semi-infinite programming and survey its wide application range. We then review numerical methods from literature and present new promising approaches from ITWM. In the second part of the talk we give a detailed numerical comparison of several methods on basis of an exhaustive set of test problem, partly stemming from real-world applications. The focus of this comparison is on the performance of an ITWM solver opposing the other introduced numerical methods concerning running time, needed iterations, and accuracy. In doing so we investigate the behaviour of the implemented solvers also with respect to different mathematical environments like convexity and dimensionality.