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Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization

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  • Elena Constantin

    (University of Pittsburgh at Johnstown)

Abstract

In this paper, we give necessary conditions for the existence of a strict local minimum of order two for multiobjective optimization problems with equality and inequality constraints. We suppose that the objective function and the active inequality constraints are only locally Lipschitz. We consider both regular equality constraints and degenerate equality constraints. This article could be considered as a continuation of [E. Constantin, Necessary Conditions for Weak Efficiency for Nonsmooth Degenerate Multiobjective Optimization Problems, J. Global Optim, 75, 111-129, 2019]. We introduce a constraint qualification and a regularity condition, and we show that under each of them, the dual necessary conditions for a weak local minimum of the aforementioned article become of Kuhn-Tucker type.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-021-01016-z
    DOI: 10.1007/s10898-021-01016-z
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    References listed on IDEAS

    as
    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. 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.
    5. 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.
    6. 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.
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