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Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization

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Listed:
  • Meijia Yang

    (University of Science and Technology Beijing)

  • Shu Wang

    (North China Electric Power University)

  • Yong Xia

    (Beihang University)

Abstract

We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02031-0
    DOI: 10.1007/s10957-022-02031-0
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    References listed on IDEAS

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    1. N. Dinh & V. Jeyakumar, 2014. "Rejoinder on: Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 41-44, April.
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    3. N. Dinh & V. Jeyakumar, 2014. "Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-22, April.
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    6. 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.
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