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Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces

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  • Xi Yin Zheng

    (Yunnan University)

  • Runxin Li

    (Yunnan University)

Abstract

In the Hilbert space case, in terms of proximal normal cone and proximal coderivative, we establish a Lagrange multiplier rule for weak approximate Pareto solutions of constrained vector optimization problems. In this case, our Lagrange multiplier rule improves the main result on vector optimization in Zheng and Ng (SIAM J. Optim. 21: 886–911, 2011). We also introduce a notion of a fuzzy proximal Lagrange point and prove that each Pareto (or weak Pareto) solution is a fuzzy proximal Lagrange point.

Suggested Citation

  • Xi Yin Zheng & Runxin Li, 2014. "Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 665-679, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-012-0259-3
    DOI: 10.1007/s10957-012-0259-3
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    References listed on IDEAS

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    1. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    2. X. Q. Yang & V. Jeyakumar, 1997. "First and Second-Order Optimality Conditions for Convex Composite Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 209-224, October.
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