A truncated three-term conjugate gradient method with complexity guarantees with applications to nonconvex regression problem

Abstract

In this paper, a truncated three-term conjugate gradient method is proposed for nonconvex unconstrained optimization. At each iteration, the search direction generated by this method is sufficiently descent independent of any line search. We investigate its global convergence with Wolfe line search under the standard assumptions. Moreover, we present its complexity analysis under the objective function with the Lipschitz continuously gradient and Armijo line search which implies that the proposed method is also globally convergent with Armijo line search. A remarkable point about its complexity is that the proposed method possesses the same complexity order as the classical gradient descent method without any restart strategy. Finally, the proposed method is applied to solve the nonconvex robust regression problems. Numerical results show that the proposed method is efficient.