Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. A transformationbased discretization method for solving general semiinfinite optimization problems
 Mathematical methods of operations research 93 (2021), Nr.1, S.83114 ISSN: 14322994 ISSN: 03409422 

 Englisch 
 Zeitschriftenaufsatz, Elektronische Publikation 
 Fraunhofer ITWM () 
Abstract
Discretization methods are commonly used for solving standard semiinfinite optimization (SIP) problems. The transfer of these methods to the case of general semiinfinite optimization (GSIP) problems is difficult due to the xdependence of the infinite index set. On the other hand, under suitable conditions, a GSIP problem can be transformed into a SIP problem. In this paper we assume that such a transformation exists globally. However, this approach may destroy convexity in the lower level, which is very important for numerical methods. We present in this paper a solution approach for GSIP problems, which cleverly combines the above mentioned two techniques. It is shown that the convergence results for discretization methods in the case of SIP problems can be transferred to our transformationbased discretization method under suitable assumptions on the transformation. Finally, we illustrate the operation of our approach as well as its performance on several examples, including a problem of volumemaximal inscription of multiple variable bodies into a larger fixed body, which has never before been considered as a GSIP test problem.