求解一类凸多目标规划最小弱有效解的填充函数法 A Filled Function Method of Finding Weak Efficient Mi-nimizer for Convex Multi-Objective Optimization

摘要

针对一类目标函数为凸向量值函数且约束为箱子集的多目标规划，先利用线性加权和法将其转化为非凸单目标规划，再利用填充函数法求得该单目标规划的全局最优解，从而得到原规划的最小弱有效解。To a kind of multi-objective optimization problem, which objective function is convex vector function and which constraints are box sets, firstly we use linear weighted method to turn it into nonconvex single-objective optimization problem, secondly we get the global minimizer of the single-objective optimi-zation problem by implying the filled function method, then we attain the weak efficient minimizer of the prime multi-objective optimization problem.