  In this paper, in order to find critical points of vector-valued functions
with respect to the partial order induced by a closed, convex, and pointed cone
with nonempty interior, we propose a nonlinear modified Polak-Ribiere-Polyak
type conjugate gradient method with a nonnegative conjugate parameter. We show
that the search direction in our method satisfies the sufficient descent
condition independent of any line search. Furthermore, under mild assumptions,
we obtain the results of global convergence with the standard Wolfe line search
conditions as well as the standard Armijo line search strategy without
convexity assumption of the objective functions. Computational experiments are
given to show the effectiveness of the proposed method.
