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Sum-of-Squares Relaxations in Robust DC Optimization and Feature Selection

Author

Listed:
  • Vaithilingam Jeyakumar

    (University of New South Wales)

  • Gue Myung Lee

    (Pukyong National University)

  • Jae Hyoung Lee

    (Pukyong National University)

  • Yingkun Huang

    (University of New South Wales)

Abstract

This paper presents sum-of-squares (SOS) relaxation results to a difference-of-convex-max (DC-max) optimization involving SOS-convex polynomials in the face of constraint data uncertainty and their applications to robust feature selection. The main novelty of the present work in relation to the recent research in robust convex and DC optimization is the derivation of a new form of minimally exact SOS relaxations for robust DC-max problems. This leads to the identification of broad classes of robust DC-max problems with finitely exact SOS relaxations that are numerically tractable. They allow one to find the optimal values of these classes of DC-max problems by solving a known finite number of semi-definite programs (SDPs) for certain concrete cases of commonly used uncertainty sets in robust optimization. In particular, we derive relaxation results for a class of robust fractional programs. Also, we provide a finitely exact SDP relaxation for a DC approximation problem of an NP-hard robust feature selection model which gives computable upper bounds for the global optimal value.

Suggested Citation

  • Vaithilingam Jeyakumar & Gue Myung Lee & Jae Hyoung Lee & Yingkun Huang, 2024. "Sum-of-Squares Relaxations in Robust DC Optimization and Feature Selection," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 308-343, January.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02312-2
    DOI: 10.1007/s10957-023-02312-2
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    References listed on IDEAS

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    1. Daniel Woolnough & Niroshan Jeyakumar & Guoyin Li & Clement T Loy & Vaithilingam Jeyakumar, 2022. "Robust Optimization and Data Classification for Characterization of Huntington Disease Onset via Duality Methods," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 649-675, June.
    2. Dunbar, Michelle & Murray, John M. & Cysique, Lucette A. & Brew, Bruce J. & Jeyakumar, Vaithilingam, 2010. "Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment," European Journal of Operational Research, Elsevier, vol. 206(2), pages 470-478, October.
    3. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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