Some descent Dai-Liao-type conjugate gradient methods for vector optimization

Abstract

Conjugate gradient methods play a crucial role in solving unconstrained optimization problems and have recently been extended to vector optimization problems (VOPs). This paper introduces four conjugate gradient methods for finding critical points of vector-valued functions with respect to the partial order induced by a closed, convex, and pointed cone with nonempty-interior, inspired by the Dai–Liao method. Initially, two Dai–Liao-type conjugate gradient methods are proposed. While these methods do not guarantee a descent direction, they are proven to converge under the assumption that a descent direction exists. These methods are further refined into modified versions that satisfy the sufficient descent condition. By employing the Wolfe line search, the sufficient descent condition is satisfied, and global convergence is achieved without requiring regular restarts or assumptions of convexity on the objective functions. Numerical experiments are conducted to demonstrate the effectiveness of the proposed methods with detailed implementation and results provided.