Global Convergence and Rate Analysis of the Steepest Descent Method for Uncertain Multiobjective Optimization via a Robust Optimization Approach

Abstract

In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global convergence and the rate of convergence of the steepest descent algorithm. To bridge this gap, we provide rigorous proofs for both global convergence and the linear convergence rate of the steepest descent algorithm. Global convergence analysis strengthens the theoretical foundation of the steepest descent method for uncertain multiobjective optimization problems, offering deeper insights into its efficiency and robustness across a broader class of optimization problems. These findings enhance the method's practical applicability and contribute to the advancement of robust optimization techniques.