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On the S-procedure and Some Variants

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  • Kürşad Derinkuyu
  • Mustafa Pınar

Abstract

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization. Copyright Springer-Verlag 2006

Suggested Citation

  • Kürşad Derinkuyu & Mustafa Pınar, 2006. "On the S-procedure and Some Variants," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 55-77, August.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:1:p:55-77
    DOI: 10.1007/s00186-006-0070-8
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    References listed on IDEAS

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    1. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Luo, Z-Q & Sturm, J.F. & Zhang, S., 2003. "Multivariate Nonnegative Quadratic Mappings," Discussion Paper 2003-7, Tilburg University, Center for Economic Research.
    4. Luo, Z-Q & Sturm, J.F. & Zhang, S., 2003. "Multivariate Nonnegative Quadratic Mappings," Other publications TiSEM 77619783-0422-424b-8dc7-2, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Huu-Quang Nguyen & Ruey-Lin Sheu, 2019. "Geometric properties for level sets of quadratic functions," Journal of Global Optimization, Springer, vol. 73(2), pages 349-369, February.
    2. Arash Gourtani & Tri-Dung Nguyen & Huifu Xu, 2020. "A distributionally robust optimization approach for two-stage facility location problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 141-172, June.
    3. Meijia Yang & Shu Wang & Yong Xia, 2022. "Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 353-363, July.

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