In this thesis , some topics in vector optimization theory with set - valued maps are discussed . the concept of generalized subconvexlike set - valued map is defined , and some important properties of the new concept are discussed in linear space . under the assuption of generalized subconvexlikeness , a gordan - farkas type alternative theorem is proved 在线性空间中定义了广义次似凸集值映射的概念，并讨论了它的一些重要性质。在广义次似凸性假设下，证明了gordan - farkas型的择一性定理。
General convex sets and convex functions : g - convex sets and g - convcx functions are investigated , some properties of which arc achieved , the cti - tcrions of g - convcx functions and g - quasiconvcx functions arc given , the theory of general convexity is deepen : two kinds of general variational inequality problems are studied 讨论了一类广义的凸集和凸函数： g -凸集和g -凸函数，得出了若干性质，给出了g -凸函数和g -拟凸函数的判别准则，丰富了广义凸性的内容；研究了两类广义的变分不等式问题。
Liu and wu ( ref . 26 ) presented sufficient conditions and proposed three dual models for the generalized fractional programming problem with - pseudoinvexity and - quasi - invexity in ref . 26 . preda ( ref . 27 ) introduced generalized ( f , ) - convexity , an extension of f - convexity and generalized - convexiry ( ref . 28 - 29 ) , relative results are also given for multiobjective programming problems 而preda在文献[ 27 ]中，又引入了推广的( f ， )一凸性，它是f ?凸性和推广的?凸性(见文献[ 28 - 29 ]的结合和延伸) ，同时给出了一些相关结果。
