Accelerated nonmonotone line search technique for multiobjective optimization

¹ UCLouvain, Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Belgium
² Faculty of Engineering, Free University of Bozen-Bolzano, Piazza Università 5, 39100 Bolzano, Italy
³ Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363 Semnan, Iran

^* Corresponding author: zohreh.aminifard@uclouvain.be

Received: 25 January 2023
Accepted: 30 January 2024

Abstract

In order to increase the probability of applying more recent information, a forgetting factor is embedded in the nonmonotone line search technique for minimization of the multiobjective problem concerning the partial order induced by a closed, convex, and pointed cone. The method is shown to be globally convergent without convexity assumption on the objective function. Moreover, to improve behavior of the classical steepest descent method, an accelerated scheme is presented. Ultimately, computational advantages of the algorithms are depicted on a class of standard test problems.