【摘要】 光滑多目标规划问题是近几年研究的热点问题，本研究利用G-ρ不变凸函数，定义了f_i-v_i g_i (·)不变凸、不变拟凸和不变伪凸函数。并利用新函数研究了不变凸分式规划的对偶问题，得到了几个对偶条件，把G-不变凸整式规划的相关结论推广到分式规划，拓展G-不变凸函数研究范围。更多还原

【Abstract】 Nonsmooth multi-objective programming is a hot topic in recent years. By G-ρ invex functions, a class of f_i-v_i g_i (·)invex, quasi invex and pseudo invex functions were defined. The duality conditions of invex fractional programming were researched, and some dual conditions were obtained, many important conclusions on G invex integral programming were generalized to fractional programming, the research scope of G invex functions were extended.更多还原