A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization

A novel Polak-Ribière-Polyak (PRP) type conjugate gradient method is proposed to solve a nonconvex vector optimization. This variant is a nontrivial extension of a PRP type conjugate gradient method from the scalar case to the vector case. We construct a new nonnegative conjugate parameter avoiding the usual truncation of conjugate gradient method. The search direction in the new PRP type conjugate gradient method is proved to satisfy the sufficient descent condition without involving any line search. The globally convergent results of the novel conjugate gradient method are derived under the standard Wolfe line search as well as the Armijo line search strategy without convexity assumption of the objective functions. Besides, the iterative sequence generated by the proposed method is also proved to be weakly convergent to some weak Pareto optimal solution of the vector optimization problem under the cone-pseudoconvexity assumption. Numerical experiments also manifest the validity of the proposed novel method. The gained results improve the corresponding results of (SIAM J Optim 28:2690–2720, 2018 and Comput Optim Appl 86:457–489, 2023).