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An approximate strong KKT condition for multiobjective optimization

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  • Min Feng

    (Chongqing University)

  • Shengjie Li

    (Chongqing University)

Abstract

In this paper, we introduce a sequential approximate strong Karush–Kuhn–Tucker (ASKKT) condition for a multiobjective optimization problem with inequality constraints. We show that each local efficient solution satisfies the ASKKT condition, but weakly efficient solutions may not satisfy it. Subsequently, we use a so-called cone-continuity regularity (CCR) condition to guarantee that the limit of an ASKKT sequence converges to an SKKT point. Finally, under the appropriate assumptions, we show that the ASKKT condition is also a sufficient condition of properly efficient points for convex multiobjective optimization problems.

Suggested Citation

  • Min Feng & Shengjie Li, 2018. "An approximate strong KKT condition for multiobjective optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 489-509, October.
    • Handle: RePEc:spr:topjnl:v:26:y:2018:i:3:d:10.1007_s11750-018-0491-6
    DOI: 10.1007/s11750-018-0491-6
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    References listed on IDEAS

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    1. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
    2. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2016. "Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 70-89, October.
    3. 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.
    4. Gabriel Haeser & María Laura Schuverdt, 2011. "On Approximate KKT Condition and its Extension to Continuous Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 528-539, June.
    5. G. Bigi & M. Pappalardo, 1999. "Regularity Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 83-96, July.
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    Cited by:

    1. Gabriele Eichfelder & Leo Warnow, 2021. "Proximity measures based on KKT points for constrained multi-objective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 63-86, May.
    2. Roberto Andreani & Ellen H. Fukuda & Gabriel Haeser & Daiana O. Santos & Leonardo D. Secchin, 2024. "Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 1-33, January.
    3. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    4. G. A. Carrizo & N. S. Fazzio & M. D. Sánchez & M. L. Schuverdt, 2024. "Scaled-PAKKT sequential optimality condition for multiobjective problems and its application to an Augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 89(3), pages 769-803, December.
    5. Javier Gomez & Cesar Alfaro & Felipe Ortega & Javier M. Moguerza & Maria Jesus Algar & Raul Moreno, 2024. "Adapting support vector optimisation algorithms to textual gender classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 463-488, October.

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