中文摘要：

在弧连通锥-凸假设下讨论Hausdorff局部凸空间中的一类数学规划的最优性条件问题.首先,利用择一定理得到了锥约束标量优化问题的一个必要最优性条件.其次,利用凸集分离定理证明了无约束向量优化问题关于弱极小元的标量化定理和一个一致的充分必要条件.所得结果深化和丰富了最优化理论及其应用的内容.

英文摘要：

This note deals with a kind of mathematical programming problems where all functions involved are arcwise connected cone-convex in HausdorfF locally convex spaces.First,by using the alternative theorem,a theorem of optimality necessary condition for a scalar optimization problem with cone-constrained is established.Then,The scalarization theorem and the unified necessary and sufficient optimality conditions are proposed for weakly minimum in a vector optimization problem through the separation theorem.The results deepen and enrich the content of optimization theory and application.