Volume 42 Issue 9
Sep.  2021
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ZENG Yue, PENG Zaiyun, LIANG Renli, SHAO Chongyang. Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets[J]. Applied Mathematics and Mechanics, 2021, 42(9): 958-967. doi: 10.21656/1000-0887.410244
Citation: ZENG Yue, PENG Zaiyun, LIANG Renli, SHAO Chongyang. Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets[J]. Applied Mathematics and Mechanics, 2021, 42(9): 958-967. doi: 10.21656/1000-0887.410244

Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

doi: 10.21656/1000-0887.410244
Funds:

The National Natural Science Foundation of China(11301571)

  • Received Date: 2020-12-17
  • Rev Recd Date: 2021-01-22
  • Available Online: 2021-09-29
  • The stability of vector optimization problems under approximate equilibrium constraints (AOPVF) via free-disposal sets was discussed. Firstly, the Berge-semicontinuity of the constraint set mapping and the closedness, the convexity and the compactness of the constraint set were obtained with the weaker convexity assumption. Moreover, under the assumption of Gamma-convergence for the objective functional sequences, the lower Painlevé-Kuratowski convergence of the weak efficient solution set and the Berge-semicontinuity of weak efficient solution mappings for AOPVF were obtained respectively. Some examples illustrate that the results are new and meaningful.
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