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Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization

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Abstract

Using the idea of upper convexificators, we propose constraint qualifications and study existence and boundedness of the Kuhn-Tucker multipliers for a nonsmooth multiobjective optimization problem with inequality constraints and an arbitrary set constraint. We show that, at locally weak efficient solutions where the objective and constraint functions are locally Lipschitz, the constraint qualifications are necessary and sufficient conditions for the Kuhn-Tucker multiplier sets to be nonempty and bounded under certain semiregularity assumptions on the upper convexificators of the functions.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Mathematical Sciences, Jilin University, Changchun, China

    X. F. Li

  2. BJNU-HKBU United International College, Zhuhai, China

    J. Z. Zhang

Authors
  1. X. F. Li
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  2. J. Z. Zhang
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Corresponding author

Correspondence to X. F. Li.

Additional information

Communicated by H.P. Benson.

The study was supported by the National Science Foundation of China and Program 985 of Jilin University.

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Li, X.F., Zhang, J.Z. Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization. J Optim Theory Appl 145, 373–386 (2010). https://doi.org/10.1007/s10957-009-9644-y

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  • DOI: https://doi.org/10.1007/s10957-009-9644-y

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