Fast Accelerated Proximal Gradient Method with New Extrapolation Term for Multiobjective Optimization

2025/07/09 by Cheng-Zhi Anna Huang, Huang, Chengzhi
Engineering · Mathematics · #Optical Systems and Laser Technology #Advanced optical system design #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2507.06737

Abstract

In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term 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.

Citations

• The convergence rate of the accelerated proximal gradient algorithm for Multiobjective Optimization is faster than O(1/k²)
• Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-like Systems
• Monotonicity for Multiobjective Accelerated Proximal Gradient Methods
• A globally convergent fast iterative shrinkage-thresholding algorithm with a new momentum factor for single and multi-objective convex optimization

Related

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