A proximal gradient method with adaptive backtracking for weakly smooth multiobjective optimization
TL;DR
The proposed proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have Holder continuous gradients and the algorithm accepts coercer stationarity measure compared to existing methods is established.
Abstract
In this paper, we propose a proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have H\"older continuous gradients. The proposed method is parameter-free as we do not require prior knowledge of parameters related to the weak smoothness of the objective function; the proposed linesearch finds an appropriate step-size that adapts to the weak smoothness. The complexity guarantee analyzed in this paper for the non-convex case is compatible with related works and our algorithm accepts coercer stationarity measure compared to existing methods. We also establish a novel complexity result for the convex case which improves the one in non-convex case.