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A semi-infinite approach to design centering

In: Optimization with Multivalued Mappings

Author

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  • Oliver Stein

    (RWTH Aachen University)

Abstract

Summary We consider design centering problems in their reformulation as general semi-infinite optimization problems. The main goal of the article is to show that the Reduction Ansatz of semi-infinite programming generically holds at each solution of the reformulated design centering problem. This is of fundamental importance for theory and numerical methods which base on the intrinsic bilevel structure of the problem. For the genericity considerations we prove a new first order necessary optimality condition in design centering. Since in the course of our analysis also a certain standard semi-infinite programming problem turns out to be related to design centering, the connections to this problem are studied, too.

Suggested Citation

  • Oliver Stein, 2006. "A semi-infinite approach to design centering," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 209-228, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-34221-4_10
    DOI: 10.1007/0-387-34221-4_10
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    Citations

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    Cited by:

    1. Stuart M. Harwood & Paul I. Barton, 2017. "How to solve a design centering problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 215-254, August.
    2. Haase, Sabrina & Süss, Philipp & Schwientek, Jan & Teichert, Katrin & Preusser, Tobias, 2012. "Radiofrequency ablation planning: An application of semi-infinite modelling techniques," European Journal of Operational Research, Elsevier, vol. 218(3), pages 856-864.
    3. Harald Günzel & Hubertus Jongen & Oliver Stein, 2007. "On the closure of the feasible set in generalized semi-infinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(3), pages 271-280, September.
    4. Volker Maag, 2015. "A collision detection approach for maximizing the material utilization," Computational Optimization and Applications, Springer, vol. 61(3), pages 761-781, July.
    5. Jan Schwientek & Tobias Seidel & Karl-Heinz Küfer, 2021. "A transformation-based discretization method for solving general semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 83-114, February.
    6. Hatim Djelassi & Alexander Mitsos, 2017. "A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs," Journal of Global Optimization, Springer, vol. 68(2), pages 227-253, June.
    7. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    8. O. Stein & A. Winterfeld, 2010. "Feasible Method for Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 419-443, August.
    9. Hatim Djelassi & Moll Glass & Alexander Mitsos, 2019. "Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints," Journal of Global Optimization, Springer, vol. 75(2), pages 341-392, October.

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