DeepAI

# Convergence Rate Analysis of Accelerated Forward-Backward Algorithm with Generalized Nesterov Momentum Scheme

Nesterov's accelerated forward-backward algorithm (AFBA) is an efficient algorithm for solving a class of two-term convex optimization models consisting of a differentiable function with a Lipschitz continuous gradient plus a nondifferentiable function with a closed form of its proximity operator. It has been shown that the iterative sequence generated by AFBA with a modified Nesterov's momentum scheme converges to a minimizer of the objective function with an o(1/k^2) convergence rate in terms of the function value (FV-convergence rate) and an o(1/k) convergence rate in terms of the distance between consecutive iterates (DCI-convergence rate). In this paper, we propose a more general momentum scheme with an introduced power parameter ω∈(0,1] and show that AFBA with the proposed momentum scheme converges to a minimizer of the objective function with an o(1/k^2ω) FV-convergence rate and an o(1/k^ω) DCI-convergence rate. The generality of the proposed momentum scheme provides us a variety of parameter selections for different scenarios, which makes the resulting algorithm more flexible to achieve better performance. We then employ AFBA with the proposed momentum scheme to solve the smoothed hinge loss ℓ_1-support vector machine model. Numerical results demonstrate that the proposed generalized momentum scheme outperforms two existing momentum schemes.

• 3 publications
• 12 publications
• 1 publication
05/11/2022

### A globally convergent fast iterative shrinkage-thresholding algorithm with a new momentum factor for single and multi-objective convex optimization

Convex-composite optimization, which minimizes an objective function rep...
02/07/2023

### Convergence rates for momentum stochastic gradient descent with noise of machine learning type

We consider the momentum stochastic gradient descent scheme (MSGD) and i...
06/18/2020

### Improving the Convergence Rate of One-Point Zeroth-Order Optimization using Residual Feedback

Many existing zeroth-order optimization (ZO) algorithms adopt two-point ...
08/20/2021

### Practical and Fast Momentum-Based Power Methods

The power method is a classical algorithm with broad applications in mac...
10/24/2019

### Efficient Computation of Kubo Conductivity for Incommensurate 2D Heterostructures

Here we introduce a numerical method for computing conductivity via the ...
02/28/2020

### Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives

We analyze the convergence rate of various momentum-based optimization a...
10/22/2021

### GPU-Accelerated Forward-Backward algorithm with Application to Lattice-Free MMI

We propose to express the forward-backward algorithm in terms of operati...