Abstract: Firstly, the existence of three kinds of D-η-properly semi-prequasiinvex mappings are verified with two examples. Then, two results are obtained, that is, the local efficient solution of multiobjective optimization is the global efficient solution and the local weak efficient solution of multiobjective optimization is the global weak efficient solution under D-η-properly semistrict(strict) semi-prequasiinvexity. They are verified by two examples. Lastly, the unicities are established about the global weak efficient solution and the local weak efficient solution of multiobjective optimization under D-η-properly strcit semi-prequasiinvexity.

Key words: D-η-properly semi-prequasiinvex mapping, semi-connected set, multiobjective optimization

摘要： 首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。