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<p>This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization. A type of directional derivatives for a multiobjective function is proposed, and with this notion characterizations of strict local minima of order <i>k</i> for a multiobjective optimization problem with a nonempty set constraint are established, generalizing the corresponding scalar case obtained by Studniarski [3]. Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives, which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones. Many examples are given to illustrate them there.</p>

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Higher-order optimality conditions for multiobjective optimization through a new type of directional derivatives

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Zheng-gang Huang

摘要

This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization. A type of directional derivatives for a multiobjective function is proposed, and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established, generalizing the corresponding scalar case obtained by Studniarski [3]. Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives, which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones. Many examples are given to illustrate them there.