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

Author

Listed:
  • S. K. Mishra

    (Banaras Hindu University)

  • B. B. Upadhyay

    (Banaras Hindu University)

  • Le Thi Hoai An

    (University Paul Verlaine of Metz)

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.

Suggested Citation

  • S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0313-9
    DOI: 10.1007/s10957-013-0313-9
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    References listed on IDEAS

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    1. Jeyakumar, V. & Lee, G.M. & Dinh, N., 2006. "Characterizations of solution sets of convex vector minimization problems," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1380-1395, November.
    2. V. Jeyakumar & G. M. Lee & N. Dinh, 2004. "Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 83-103, October.
    3. D. Aussel, 1998. "Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 29-45, April.
    4. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    5. Komlosi, S., 1993. "First and second order characterizations of pseudolinear functions," European Journal of Operational Research, Elsevier, vol. 67(2), pages 278-286, June.
    6. X. Q. Yang, 1997. "Vector Variational Inequality and Vector Pseudolinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 729-734, December.
    7. J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
    8. K. O. Kortanek & J. P. Evans, 1967. "Pseudo-Concave Programming and Lagrange Regularity," Operations Research, INFORMS, vol. 15(5), pages 882-891, October.
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    Cited by:

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    2. Kin Keung Lai & Shashi Kant Mishra & Sanjeev Kumar Singh & Mohd Hassan, 2022. "Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems," Mathematics, MDPI, vol. 10(15), pages 1-16, August.

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