凸复合多目标优化问题的二阶最优性条件

Second-order Optimality Conditions for Convex Composite Multiobjective Optimization Problem

研究了闭凸约束下凸复合多目标优化的最优性条件，利用标量凸复合优化问题的最近结果，获得了二阶必要条件；并且通过把标量化问题转化为带有非有限值凸函数的凸复合优化问题，导出了二阶充分条件．

A convex composite multiobjective optimization problem,which subject to a closed con-vex constraint,is studied.A second-order necessary condition is obtained by using a recent result for scalar convex composite optimization.Moreover,a second order sufficient condition was derived by transforming the scalarization problem into a convex composite optimization problem with a nonfinite-valued convex function.