A study of Liu-Storey conjugate gradient methods for vector optimization

•This work presents a study of Liu-Storey nonlinear conjugate gradient methods to solve vector optimization problems.•We test our proposed algorithms on a set of problems taken from the multiobjective optimization literature.•The Liu-Storey nonlinear conjugate gradient methods are efficient to find critical Pareto points. 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 results and numerical experiments are presented.