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

Conjugate gradient methods are considered vital for solving unconstrained single-objective optimization problems and have recently been extended to vector optimization problems (VOPs). In this paper, four conjugate gradient methods for VOPs, inspired by the Dai-Liao method, are introduced. Initially, two Dai-Liao-type conjugate gradient methods are proposed, which, although they do not guarantee a descent direction, are shown to converge under the assumption of descent direction. These methods are refined to create two 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.