- A transformation-based discretization method for solving general semi-infinite optimization problems Jan Schwientek (Jan.Schwientekitwm.fraunhofer.de) Tobias Seidel (Tobias.Seidelitwm.fraunhofer.de) Karl-Heinz Küfer (Karl-Heinz.Kueferitwm.fraunhofer.de) Abstract: Discretization methods are commonly used for solving standard semi-infinite optimization (SIP) problems. The transfer of these methods to the case of general semi-infinite optimization (GSIP) problems is difficult due to the $x$-dependence 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 \emph{transformation-based discretization method} under suitable assumptions on the transformation. Finally, we illustrate the operation of our approach as well as its performance on three examples, including a problem of volume-maximal inscription of multiple variable bodies into a larger fixed body, which has never before been considered as a GSIP test problem. Keywords: semi-infinite optimization, discretization, coordinate transformation, design centering, inscribing Category 1: Infinite Dimensional Optimization (Semi-infinite Programming ) Citation: Preprint, Fraunhofer ITWM, Fraunhofer-Platz 1, D-67663 Kaiserslautern, 12/2017 Download: [PDF]Entry Submitted: 12/15/2017Entry Accepted: 12/15/2017Entry Last Modified: 02/07/2020Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.