APPROXIMATE NECESSARY CONDITIONS FOR LOCALLY WEAK PARETO-OPTIMALITY

Necessary conditions for a given point x0 to be a locally weak solutio n to the Pareto minimization problem of a vector-valued function F = ( f1,...,f(m)), F:X --> R(m), X subset-or-equal-to R(n), are presented. As noted in Ref. 1, the classical necessary condition -conv{Df1(x0) \ i = 1, . . . , m) and T(X, x0) not-equal empty set need not hold when the contingent cone T is used. We have proven, however, that a proper ly adjusted approximate version of this classical condition always hol ds. Strangely enough, the approximation for m > 2 must be weaker than for m = 2.