D-E-半预不变真拟凸映射与向量优化

D-E-Properly Semi-Prequasi-Invex Mappings and Vector Optimization

提出了一类新的向量值映射-D-E-半预不变真拟凸映射,它是D-半预不变真拟凸映射和D-E-预不变真拟凸映射的真推广.首先,举例验证了D-E半预不变真拟凸映射的存在性;其次,说明了D-E-半预不变真拟凸映射的水平集是E-半不变凸集,讨论了D-E-严格半预不变真拟凸映射和D-E-半严格半预不变真拟凸映射的关系;再次,在D-E-半严格(严格)半预不变真拟凸性下,得出了向量优化问题的E-局部有效解为E-全局有效解,E-局部弱有效解为E-全局弱有效解,并举例验证了所得结果;最后,在D-E-严格半预不变真拟凸性下,建立了向量优化问题的E-全局弱有效解和E-局部弱有效解的唯一性刻画.

In this paper,a class of new vector-valued mapping-D-E-properly semiprequasi-invex mapping is put forward,it is true generalization of D-properly semiprequasi-invex mapping and D-E-properly prequasi-invex mapping.Firstly,examples are given to verified the existence of D-E-properly semi-prequasi-invex mappings;Secondly,it is illustrated that the level set of D-E-properly semi-prequasi-invex mapping is an E-semi-invex set,the equivalent relation between D-E-properly semi-strictly semi-prequasi-invex mapping and D-E-properly strictly semi-prequasi-invex mapping is discussed.Thirdly,two results are obtained,that is,the E-local efficient solution of vector optimization problem is the E-global efficient solution and the E-local weak efficient solution of vector optimization problem is the E-global weak efficient solution under D-E-properly semistrictly (strictly)semi-prequasi-invexity,they are verified with two examples;Lastly,the unicity is established about the E-global weak efficient solution and the E-local weak efficient solution of vector optimization problem under D-E-properly strictly semi-prequasi-invexity.