Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems

LI Xiao-yan; GAO Ying

doi:10.3879/j.issn.1000-0887.2015.06.011

Volume 36 Issue 6

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LI Xiao-yan, GAO Ying. Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems[J]. Applied Mathematics and Mechanics, 2015, 36(6): 668-676. doi: 10.3879/j.issn.1000-0887.2015.06.011

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Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems

doi: 10.3879/j.issn.1000-0887.2015.06.011

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, P.R.China

Funds: The National Natural Science Foundation of China(11201511；11271391；11431004)

Received Date: 2014-12-08
Rev Recd Date: 2015-05-05
Publish Date: 2015-06-15

Abstract

Abstract

First, linear scalarization of the proximal proper efficient points to a closed set was presented under the generalized convexity assumption, and the equivalency among the proximal proper efficiency, Benson proper efficiency and Borwein proper efficiency in multiobjective optimization problems was proved. Second, the optimality conditions for multiobjective optimization problems were obtained through application of these results to the problems. Finally, the fuzzy optimality conditions for the proximal proper efficient solutions were given with the proximal subdifferential.
- proximal normal cone,
- multiobjective optimization problem,
- proximal proper efficiency,
- optimality-condition

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References(18)

References

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