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<p>We provide sharp and explicit characterizations of the normal cone to sublevel sets of suprema of arbitrary functions, expressed exclusively in terms of subdifferentials of the data functions. In the convex case, the resulting formulas involve the approximate and exact subdifferentials of the individual data functions at the nominal and nearby points. In contrast, the quasiconvex framework requires the use of the Fréchet subdifferential of these data functions but evaluated at nearby points. These results are applied to derive optimality conditions for infinite convex and quasiconvex optimization problems.</p>

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Normal cones to sublevel sets of suprema of convex and quasiconvex functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月30日

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  • Stephanie Caro,
  • Rafael Correa,
  • Abderrahim Hantoute

摘要

We provide sharp and explicit characterizations of the normal cone to sublevel sets of suprema of arbitrary functions, expressed exclusively in terms of subdifferentials of the data functions. In the convex case, the resulting formulas involve the approximate and exact subdifferentials of the individual data functions at the nominal and nearby points. In contrast, the quasiconvex framework requires the use of the Fréchet subdifferential of these data functions but evaluated at nearby points. These results are applied to derive optimality conditions for infinite convex and quasiconvex optimization problems.