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<p>Novel classes of generalized convexity, specifically including <i>G</i>–<i>V</i>-semipreinvexity and semistrictly <i>G</i>–<i>V</i>-semipreinvexity, are introduced in this paper. Under these newly defined convexity, necessary and sufficient optimality conditions for semi-infinite minimax optimization problems are established. Furthermore, Mond–Weir type and Wolfe type dual models are developed for the primal problem. Rigorous proofs demonstrate that duality theorems hold consistently within the same framework. The developed theory can be applied across multiple domains. It can be employed in uncertainty and minimax optimization, particularly in aerodynamic design and financial risk modeling. Extensions of the theory can also be made to robust optimization frameworks and machine learning fields.</p>

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Optimality and duality in semi-infinite minimax programming with G–V semipreinvexity

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Junyao Ren,
  • Ke Su

摘要

Novel classes of generalized convexity, specifically including G–V-semipreinvexity and semistrictly G–V-semipreinvexity, are introduced in this paper. Under these newly defined convexity, necessary and sufficient optimality conditions for semi-infinite minimax optimization problems are established. Furthermore, Mond–Weir type and Wolfe type dual models are developed for the primal problem. Rigorous proofs demonstrate that duality theorems hold consistently within the same framework. The developed theory can be applied across multiple domains. It can be employed in uncertainty and minimax optimization, particularly in aerodynamic design and financial risk modeling. Extensions of the theory can also be made to robust optimization frameworks and machine learning fields.