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A transformation-based discretization method for solving general semi-infinite optimization problems

Jan Schwientek (Jan.Schwientek***at***itwm.fraunhofer.de)
Tobias Seidel (Tobias.Seidel***at***itwm.fraunhofer.de)
Karl-Heinz Küfer (Karl-Heinz.Kuefer***at***itwm.fraunhofer.de)

Abstract: Discretization methods are commonly used for solving standard semi-infinite optimization (SIP) problems. The transfer of these techniques to the case of general semi-infinite optimization (GSIP) problems is difficult because of the x-dependence of the infinite index set. On the other hand, under suitable conditions, a GSIP problem can be transferred into a SIP problem. 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, one of them, a problem of volume-maximal inscription of multiple variable bodies into a larger fixed body, which was never considered as GSIP test problem before.

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: 12/15/2017
Entry Accepted: 12/15/2017
Entry Last Modified: 12/18/2017

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