A vector restricted variant MVHS+ CG method based algorithm for unconstrained vector optimization problems

Abstract

Vector optimization problems are a critical class of optimization problems that find extensive application in fields such as engineering design, space exploration, and management science. Currently, the investigation into methodologies for addressing these issues forms an active area of research. In this paper, we propose a modified Hestenes–Stiefel (HS) conjugate gradient method for solving unconstrained vector optimization problems. It can be viewed as the generalization of the vector version of the HS+ conjugate gradient method. At each iteration of the algorithm, a search direction that satisfy the sufficient descent condition is generated without any line search or convexity. Global convergence of the algorithm is proved under the standard vector Wolfe line search. Numerical results show that the proposed method is effective. In particular, this method can properly generate the Pareto fronts for the test problems.