Nestorv's Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization

Abstract: In this paper, we propose a novel extrapolation coefficient scheme within the Nesterov framework and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed scheme only requires the Lipschitz constant estimate sequence to satisfy mild initial conditions, under which a key equality property can be derived to support the convergence analysis. Numerical experiments are provided to demonstrate the effectiveness and practical performance of the proposed method.