ZHAO Yong, PENG Zai-yun, ZHANG Shi-sheng. Stability of the Sets of Efficient Points of Vector-Valued Optimization Problems[J]. Applied Mathematics and Mechanics, 2013, 34(6): 643-650. doi: 10.3879/j.issn.1000-0887.2013.06.010
Citation: ZHAO Yong, PENG Zai-yun, ZHANG Shi-sheng. Stability of the Sets of Efficient Points of Vector-Valued Optimization Problems[J]. Applied Mathematics and Mechanics, 2013, 34(6): 643-650. doi: 10.3879/j.issn.1000-0887.2013.06.010

Stability of the Sets of Efficient Points of Vector-Valued Optimization Problems

doi: 10.3879/j.issn.1000-0887.2013.06.010
  • Received Date: 2013-04-27
  • Rev Recd Date: 2013-05-31
  • Publish Date: 2013-06-15
  • By using quasi C-convex function and recession cone property, the stability of efficient points sets to vector optimization problems without the assumption of compactness was established.The lower part of the Painlevé-Kuratowski convergence of the sets for efficient points of perturbed problems to the corresponding efficient sets for the vector optimization problems was obtained, where the perturbation was performed on both the objective function and the feasible set. These results extend and improve the corresponding ones in the literature (Attouch H, Riahi H. Stability results for Ekeland’s ε-variational principle and cone extremal solution; Huang X X. Stability in vector-valued and set-valued optimization), then examples are given to illustrate our main results.
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