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Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization

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  • Elena Constantin

    (University of Pittsburgh at Johnstown)

Abstract

The main goal of this paper is to give some primal and dual Karush–Kuhn–Tucker second-order necessary conditions for the existence of a strict local Pareto minimum of order two for an inequality-constrained multiobjective optimization problem. Dual Karush–Kuhn–Tucker second-order sufficient conditions are provided too. We suppose that the objective function and the active inequality constraints are only locally Lipschitz in the primal necessary conditions and only strictly differentiable in sense of Clarke at the extremum point in the dual conditions. Examples illustrate the applicability of the obtained results.

Suggested Citation

  • Elena Constantin, 2020. "Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 50-67, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01688-9
    DOI: 10.1007/s10957-020-01688-9
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    References listed on IDEAS

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    1. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    2. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    3. G. Giorgi & B. Jiménez & V. Novo, 2009. "Strong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 288-304, December.
    4. Yuan Liu & Zhi Ning & Yu Chen & Ming Guo & Yingle Liu & Nirmal Kumar Gali & Li Sun & Yusen Duan & Jing Cai & Dane Westerdahl & Xinjin Liu & Ke Xu & Kin-fai Ho & Haidong Kan & Qingyan Fu & Ke Lan, 2020. "Aerodynamic analysis of SARS-CoV-2 in two Wuhan hospitals," Nature, Nature, vol. 582(7813), pages 557-560, June.
    5. Giancarlo Bigi, 2006. "On sufficient second order optimality conditions in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 77-85, February.
    6. M. C. Maciel & S. A. Santos & G. N. Sottosanto, 2009. "Regularity Conditions in Differentiable Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 385-398, August.
    7. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    8. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    9. Vsevolod I. Ivanov, 2015. "Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 777-790, September.
    10. Do Van Luu, 2018. "Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems," Journal of Global Optimization, Springer, vol. 70(2), pages 437-453, February.
    11. Manxue You & Shengjie Li, 2017. "Separation Functions and Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 527-544, November.
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    Cited by:

    1. Elena Constantin, 2021. "Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 177-193, May.

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