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Convexifiable quadratic inequality systems: new minimax S-lemma and exact SOCPs for classes of distributionally robust optimization problems

Author

Listed:
  • Q. Y. Huang

    (University of New South Wales)

  • V. Jeyakumar

    (University of New South Wales)

  • G. Li

    (University of New South Wales)

  • D. T. K. Huyen

    (University of New South Wales
    Phenikaa University)

Abstract

This paper introduces a generalization of the powerful S-lemma, extending it to minimax quadratic functions for the first time. Notably, the convexity of the involved functions is not assumed; instead, our approach leverages the convexifiability of the associated quadratic systems. It provides various verifiable conditions to identify this convexifiability by exploiting the system’s separability. Using the new minimax S-lemma and the simultaneous diagonalization property, the paper presents exact second-order cone program reformulations for classes of distributionally robust optimization problems involving minimax quadratic functions, ensuring that they share the same optimal value and can efficiently be solved. Finally, it also provides numerical validations of our results for concrete models of insurance risk assessment, maximum revenue estimation, and option pricing under distributional uncertainty.

Suggested Citation

  • Q. Y. Huang & V. Jeyakumar & G. Li & D. T. K. Huyen, 2025. "Convexifiable quadratic inequality systems: new minimax S-lemma and exact SOCPs for classes of distributionally robust optimization problems," Journal of Global Optimization, Springer, vol. 92(3), pages 535-568, July.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:3:d:10.1007_s10898-025-01499-0
    DOI: 10.1007/s10898-025-01499-0
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    References listed on IDEAS

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    2. 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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