向量优化问题的一类高阶对偶

摘要

Meetu在文献[1]中介绍了高阶锥凸、高阶（强）锥伪凸和高阶拟凸．本文在其研究的基础上，考虑目标函数是高阶锥伪凸、约束函数是高阶锥拟凸的情况，并给出弱极小、极小的充分性条件．此外，在高阶广义凸性的假设下，建立了一类高阶对偶模型的弱对偶和强对偶结果．%introduced minimum, Higher order cone convex, pseudo convex, strongly pseudo convex and quasiconvex functions are by Meetu [ 1 ]. In the paper, higher order sufficient optimality conditions are given for a weak minimum solution of a vector optimization problem under which an objective function is higher or-der cone pseudo convex and a constraint function is higher order cone quasiconvex. Moreover, weak and strong duality theorems are established for （HD） under these new generalized convexity assumptions.