D-η-E-Semipreinvex Vector Mappings and Vector Optimization
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摘要: 提出了一类新的向量值映射——D- η -E-半预不变凸映射, 它是E-预不变凸映射与D- η -半预不变凸映射的真推广.首先, 用例子说明了E-半不变凸集、D- η -E-半预不变凸映射的存在性;然后,给出了D- η -E-半预不变凸映射的判定定理, 并讨论了D- η -E-半预不变凸映射与D- η -E-严格/半严格半预不变凸映射的关系;最后,得到了D- η -E-半严格半预不变凸映射在隐约束优化问题中的一个重要应用,并举例验证了所得结果.
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关键词:
- E-半不变凸集 /
- D-η-E-半预不变凸映射 /
- 判定定理 /
- 优化问题 /
- 应用
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.-
Key words:
- E-semi-invex set /
- D-η-E-semipreinvex mapping /
- decision criterion /
- vector optimization /
- application
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