Invexity criteria for a class of vector-valued functions

Abstract

This paper gives criteria, necessary or sufficient for a vector-valued function F = (f1, f2, …, fk) to be invex. Here each fi is of the -class (that is, each fi is a function whose gradient mapping is locally Lipschitz in a neighbourhood of x0) and the invexity of F means that F(x) − F(x0) ⊂ ˚F′(X) + Q for a fixed convex cone Q of Rk and every x near x0 (˚F′ being the Jacobian matrix of F at x0).