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Characterizations of the solution set for a class of nonsmooth optimization problems

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Abstract

In this paper, a class of nonsmooth optimization problems with inequality constraints is considered. It is shown that the Lagrangian function associated with a fixed Lagrange multiplier is constant on the solution set under suitable conditions. Then, some characterizations of the solution set of this class of optimization problems are obtained. Examples are given to illustrate our main results.

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia University, Inner Mongolia, 010021, China

    Ke Quan Zhao

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, China

    Ke Quan Zhao & Xin Min Yang

Authors
  1. Ke Quan Zhao
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  2. Xin Min Yang
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Corresponding author

Correspondence to Ke Quan Zhao.

Additional information

This work is partially supported by the National Science Foundation of China (Grants 10831009, 11126348), the Natural Science Foundation Project of Chongqing (Grants 2011BA0030), the Special Fund of Chongqing Key Laboratory (CSTC, 2011KLORSE02) and the Education Committee Research Foundation of Chongqing (KJ110625).

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Zhao, K.Q., Yang, X.M. Characterizations of the solution set for a class of nonsmooth optimization problems. Optim Lett 7, 685–694 (2013). https://doi.org/10.1007/s11590-012-0471-y

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  • DOI: https://doi.org/10.1007/s11590-012-0471-y

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