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On multiobjective optimization problems involving higher order strong convexity using directional convexificators

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  • Prachi Sachan

    (Banaras Hindu University)

  • Vivek Laha

    (Banaras Hindu University)

Abstract

In this paper, we introduce the notion of strong convexity of higher order along continuity directions based on strong convexity of higher order by Lin and Fukushima (Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl. 2003;118:67–80) and convexity along continuity directions by Dempe and Pilecka (Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Glob Optim. 2015;61:769–788). We characterize strong convexity of higher order along continuity directions of a function using the monotonicity of the associated directional convexificators. We have also studied multiobjective optimization problems involving strongly convex functions of higher order along continuity directions. We use vector variational inequalities of higher order in terms of directional convexificators to identify strict minimizers and semi-strict minimizers for the multiobjective optimization problems.

Suggested Citation

  • Prachi Sachan & Vivek Laha, 2025. "On multiobjective optimization problems involving higher order strong convexity using directional convexificators," OPSEARCH, Springer;Operational Research Society of India, vol. 62(3), pages 1200-1223, September.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:3:d:10.1007_s12597-024-00840-7
    DOI: 10.1007/s12597-024-00840-7
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    References listed on IDEAS

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    1. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
    2. G.H. Lin & M. Fukushima, 2003. "Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 67-80, July.
    3. Yogendra Pandey & S. K. Mishra, 2018. "Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators," Annals of Operations Research, Springer, vol. 269(1), pages 549-564, October.
    4. Do Luu, 2014. "Necessary and Sufficient Conditions for Efficiency Via Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 510-526, February.
    5. Stephan Dempe & Maria Pilecka, 2015. "Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming," Journal of Global Optimization, Springer, vol. 61(4), pages 769-788, April.
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