向量值映射D-η-预不变真拟凸的性质

PROPERTIES OF D-η-PROPERLY PREQUASIINVEX FUNCTION

引入了向量值映射的D-η- 预不变真拟凸等概念,在下D-半连续和上D-半连续条件下分别得到了向量值映射的D-η- 预不变真拟凸的等价命题,并讨论了向量值映射的D-η- 预不变真拟凸、D-η- 严格预不变真拟凸、D-η- 半严格预不变真拟凸的关系,证明了在一定条件下,向量优化问题(VP)的局部弱有效解一定是(VP)的全局弱有效解,这些结果推广了前人所得的相应结果。

In this paper, such definitions as .D-η-properly prequasiinvex, and D-η-properly semistrictly prequasiinvex for vector-valued maps are introduced, under the lower D-Semi-continuous condition and the upper D- Semi-continuous condition, respectively. Some equivalent propositions concerning D-η-properly prequasiinvex for vector-valued maps are obtained, and the relationsamong D-η-properry prequasiinvex, D-η-properly semistrictly prequasiinvex and D-η-properly strictly prequasiinvex are discussed. Under some conditions, the fact that the local weak efficient solution of (VP) must be the global weak efficient solution of (VP) is proved. These results generalize the corresponding results in [2, 6-9].