有效解的刻划

CHARACTERIZATION OF EFFICIENT SOLUTIONS

对于多目标问题有效解的刻划,已有许多工作,在[3]中推广了[5]中单目标凸规划的极优解的 Fritz John 型必要条件,在 Slater 型条件假定下,进一步给出了多目标非可微凸规划有效解的必要条件(本文(7),(8)).[2]在假定 Slater 型条件成立时,证明类似于[3]的条件(本文(9),(10))可成为有效解的充要条件.

This paper considers a multiobjective programming problem (P).First we provethat the problem satisfies the saddle point criteria at an efficient solution x_0 for α∈intR_+~n, iff (?)_α(0)=〈α,f(x_0)〉,(?)(0)≠(?).Next we prove that the conditions((7),(8) in this paper) of [3] are equivalent to conditions ((9),(10) in this paper) of[2],that they are also sufficient conditions for the efficient solutions,and that anefficient solution of (P) is equivalent to (7) and (8) iff (P) satisfies the saddlepoint criteria.Finally we consider Wolfe-type dual problem and prove that a dualproperty in [2] is equivalent to satisf action of the saddle point criteria.