This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying the (vector) standard Wolfe conditions. The second algorithm combines a modification in the LS conjugate parameter with a line search satisfying the (vector) strong Wolfe conditions. The third algorithm consists of a combination of the LS conjugate parameter with a new Armijo-type line search (to be proposed here for the vector setting). Global convergence of the methods under mild assumptions is established. Finally, numerical experiments illustrating the practical efficiency of the new methods and comparisons with existing algorithms are discussed.
M. L. N. Gonçalves, F. S. Lima, and L. F. Prudente, A study of Liu-Storey conjugate gradient methods for vector optimization, Federal University of Goias, 2021.