Convex Optimization

Accelerated First-Order Optimization Algorithms for Machine Learning

Numerical optimization serves as one of the pillars of machine learning. To meet the demands of big data applications, lots of efforts have been done on designing theoretically and practically fast algorithms. This paper provides a comprehensive …

Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or …

Fast gradient vector flow computation based on augmented Lagrangian method

We proposed new algorithms for GVF and GGVF computation. Our methods are comparable with the MGVF method, and are more simple. We applied the proposed methods to GVF snake for image segmentation. GVF-based anisotropic diffusion model confirms the validity of our new methods.

A Generalized Accelerated Proximal Gradient Approach for Total Variation-Based Image Restoration

This paper proposes a generalized accelerated prox- imal gradient (GAPG) approach for solving total variation (TV) based image restoration problems.