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

Thai Doan Chuong () and José Vicente-Pérez ()
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Thai Doan Chuong: Brunel University of London
José Vicente-Pérez: University of Alicante

Journal of Global Optimization, 2025, vol. 91, issue 4, No 2, 743-763

Abstract: 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.

Keywords: Conic programming; Polynomial optimization; Minimax programs; Relaxations; Duality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01465-w

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