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<p>We investigate first- and second-order optimality conditions for constrained optimization problems with interval-valued objective functions. By introducing new directional derivatives based on generalized Hukuhara differences, we establish necessary and sufficient optimality conditions. The proposed conditions extend existing results and remain applicable even when the endpoint functions of the interval are nonsmooth or nonconvex. Important statements are illustrated by examples.</p>

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First and Second-Order Conditions for Interval Optimization Problems by Using Generalized Interval Differences

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Yurilev Chalco-Cano,
  • Beatriz Hernández-Jiménez,
  • Alberto Ramos

摘要

We investigate first- and second-order optimality conditions for constrained optimization problems with interval-valued objective functions. By introducing new directional derivatives based on generalized Hukuhara differences, we establish necessary and sufficient optimality conditions. The proposed conditions extend existing results and remain applicable even when the endpoint functions of the interval are nonsmooth or nonconvex. Important statements are illustrated by examples.