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