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

• Published in: Applied mathematics and computation Vol. 425; p. 127099
• Main Authors: Gonçalves, M.L.N., Lima, F.S., Prudente, L.F.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2022
• Subjects: Conjugate gradient methods; Global convergence; Pareto efficiency; Vector optimization; Global convergence; Conjugate gradient methods; Pareto efficiency; Vector optimization
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127099

•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.