<em>D-<strong>η</strong>-E</em>-Semipreinvex Vector Mappings and Vector Optimization

PENG Zai-yun; LI Ke-ke; ZHANG Shi-sheng

doi:10.3879/j.issn.1000-0887.2014.09.008

Volume 35 Issue 9

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PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. D-η-E-Semipreinvex Vector Mappings and Vector Optimization[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008

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PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. D-η-E-Semipreinvex Vector Mappings and Vector Optimization[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008

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D-η-E-Semipreinvex Vector Mappings and Vector Optimization

doi: 10.3879/j.issn.1000-0887.2014.09.008

Funds: The National Natural Science Foundation of China(11301571; 11271389)

Received Date: 2014-04-05
Publish Date: 2014-09-15

Abstract

Abstract

A class of new vector valued generalized convex mappings—D- η -E-semipreinvex mappings, as a true generalization of the E-preinvex mappings and the D-η-semipreinvex mappings, were given. First, several examples were presented to show the existence of the E-semi-invex sets and the D- η -E-semipreinvex mappings. Second, a decision criterion for the D- η -E-semipreinvex mappings was introduced, and the relationships among the D- η -E-semipreinvexity, the D- η -E-strict semipreinvexity and the D- η -E-semistrict semipreinvexity were discussed.Finally, an important application of the D- η -E-semistrictly semipreinvexity to vector optimization with implicit constraint was discussed, then some examples were given to prove the main conclusions.
- E-semi-invex set,
- D-η-E-semipreinvex mapping,
- decision criterion,
- vector optimization,
- application

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References

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