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Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions

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Abstract

We propose two kinds of variational sets of any order for multivalued mappings and show that they are advantageous over many known generalized derivatives in the use for establishing optimality conditions. Applying these sets, we prove both necessary and sufficient optimality conditions of any order for efficiency and weak efficiency in a unified way. Many corollaries and examples are provided to show that our results include many recent existing ones. The imposed assumptions are very relaxed and the proofs are rather short in comparison with those of recent results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Thu Duc, Hochiminh City, Vietnam

    P. Q. Khanh

  2. Department of Mathematics, University of Natural Sciences of Hochiminh City, Hochiminh City, Vietnam

    N. D. Tuan

Authors
  1. P. Q. Khanh
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  2. N. D. Tuan
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Corresponding author

Correspondence to P. Q. Khanh.

Additional information

Communicated by P.L. Yu.

This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.

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Khanh, P.Q., Tuan, N.D. Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions. J Optim Theory Appl 139, 47–65 (2008). https://doi.org/10.1007/s10957-008-9415-1

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