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Conic relaxations for conic minimax convex polynomial programs with extensions and applications

Author

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  • Thai Doan Chuong

    (Brunel University of London)

  • José Vicente-Pérez

    (University of Alicante)

Abstract

In this paper, we analyze conic minimax convex polynomial optimization problems. Under a suitable regularity condition, an exact conic programming relaxation is established based on a positivity characterization of a max function over a conic convex system. Further, we consider a general conic minimax $$\rho $$ ρ -convex polynomial optimization problem, which is defined by appropriately extending the notion of conic convexity of a vector-valued mapping. For this problem, it is shown that a Karush-Kuhn-Tucker condition at a global minimizer is necessary and sufficient for ensuring an exact relaxation with attainment of the conic programming relaxation. The exact conic programming relaxations are applied to SOS-convex polynomial programs, where appropriate choices of the data allow the associated conic programming relaxation to be reformulated as a semidefinite programming problem. In this way, we can further elaborate the obtained results for other special settings including conic robust SOS-convex polynomial problems and difference of SOS-convex polynomial programs.

Suggested Citation

  • Thai Doan Chuong & José Vicente-Pérez, 2025. "Conic relaxations for conic minimax convex polynomial programs with extensions and applications," Journal of Global Optimization, Springer, vol. 91(4), pages 743-763, April.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-025-01465-w
    DOI: 10.1007/s10898-025-01465-w
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