New Set-Valued Directional Derivatives: Calculus and Optimality Conditions

Nguyen Minh Tung () and Nguyen Xuan Duy Bao ()
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Nguyen Minh Tung: Banking University of Ho Chi Minh City
Nguyen Xuan Duy Bao: University of Science

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 2, No 2, 437 pages

Abstract: Abstract In this paper, we propose a new notion called radial directional derivative and derive its existence as well as main calculus rules. Then we employ them to investigate optimality conditions for a nonsmooth vector optimization problem subjected to an inclusion constraint in Banach spaces. With a directional (Hölder) metric subregularity assumption and a constraint qualification, necessary optimality conditions for both local weak and strict solutions are given in types of Karush–Kuhn–Tucker multiplier rules. The sufficient conditions are also established for local strict solutions whenever the decision space is finite-dimensional without any convexity assumption. Examples are provided to show advantages of the presented results over recent existing ones.

Keywords: Nonsmooth optimization; Multiplier rules; Weak solution; Strict solution; Directional derivatives; Directional Hölder metric subregularity; 90C29; 90C46; 49K27 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02185-5

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