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Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems

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Abstract

This paper deals with the minimization of a class of nonsmooth pseudolinear functions over a closed and convex set subject to linear inequality constraints. We establish several Lagrange multiplier characterizations of the solution set of the minimization problem by using the properties of locally Lipschitz pseudolinear functions. We also consider a constrained nonsmooth vector pseudolinear optimization problem and derive certain conditions, under which an efficient solution becomes a properly efficient solution. The results presented in this paper are more general than those existing in the literature.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions that helped to improve the paper in its present form. The authors would like to thank Prof. Nicolas Hadjisavvas, for fruitful discussions. The second author is supported by the Council of Scientific and Industrial Research, New Delhi, India, through grant no. 09/013(0357)/2011-EMR-I.s.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, 221005, India

    S. K. Mishra & B. B. Upadhyay

  2. Laboratory of Theoretical and Applied Computer Science LITA, UFR MIM, University Paul Verlaine of Metz, Metz, France

    Le Thi Hoai An

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  1. S. K. Mishra
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  2. B. B. Upadhyay
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  3. Le Thi Hoai An
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Correspondence to S. K. Mishra.

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Communicated by Vaithilingam Jeyakumar.

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Mishra, S.K., Upadhyay, B.B. & An, L.T.H. Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems. J Optim Theory Appl 160, 763–777 (2014). https://doi.org/10.1007/s10957-013-0313-9

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