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<p>The Karush-Kuhn-Tucker (KKT)-type higher-order sufficient optimality criteria for a set-valued optimization problem ((SVOP) (P)) are established in this study using higher-order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\kappa\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation>-cone arcwise connectedness and generalized contingent epiderivative assumptions. Moreover, we formulate the Wolfe (<i>WD</i>), Mond-Weir (<i>MWD</i>), and mixed (<i>MD</i>) kinds duals for the problem (SVOP) (P) and establish the associated higher-order converse, strong, and weak duality theorems. We provide non-trivial illustrative example highlighting the significance of all the results established in this paper. Our results improve the ones which are currently available in the literature for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\kappa =0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>κ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Sufficiency and duality for set-valued optimization problems with \(\kappa\)-cone arcwise connectedness of higher-order

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Koushik Das,
  • Chandal Nahak

摘要

The Karush-Kuhn-Tucker (KKT)-type higher-order sufficient optimality criteria for a set-valued optimization problem ((SVOP) (P)) are established in this study using higher-order \(\kappa\) κ -cone arcwise connectedness and generalized contingent epiderivative assumptions. Moreover, we formulate the Wolfe (WD), Mond-Weir (MWD), and mixed (MD) kinds duals for the problem (SVOP) (P) and establish the associated higher-order converse, strong, and weak duality theorems. We provide non-trivial illustrative example highlighting the significance of all the results established in this paper. Our results improve the ones which are currently available in the literature for \(\kappa =0\) κ = 0 .