Guoyong Gu – Optimization Online

A TVSCAD approach for image deblurring with impulsive noise

Published: 2017/02/08

Nonsmooth Optimization alternating direction method of multipliers, dc programming, deblurring, impulsive noise, kl function, l1-norm, regularization, scad, total variation

We consider image deblurring problem in the presence of impulsive noise. It is known that \emph{total variation} (TV) regularization with L1-norm penalized data fitting (TVL1 for short) works reasonably well only when the level of impulsive noise is relatively low. For high level impulsive noise, TVL1 works poorly. The reason is that all data, both … Read more

Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a uniform approach

Published: 2011/10/30

Guoyong Gu

Bingsheng He

Xiao-Ming Yuan

Convex Optimization convex optimization, customized algorithms, o(1/t) convergence rate, proximal point algorithm, saddle point problem, splitting algorithms

This paper takes a uniform look at the customized applications of proximal point algorithm (PPA) to two classes of problems: the linearly constrained convex minimization problem with a generic or separable objective function and a saddle-point problem. We model these two classes of problems uniformly by a mixed variational inequality, and show how PPA with … Read more

A relaxed customized proximal point algorithm for separable convex programming

Published: 2011/08/30

Convex Optimization alternating direction method, convergence rate, convex optimization, over-relaxation, proximal point algorithm, separable structure

The alternating direction method (ADM) is classical for solving a linearly constrained separable convex programming problem (primal problem), and it is well known that ADM is essentially the application of a concrete form of the proximal point algorithm (PPA) (more precisely, the Douglas-Rachford splitting method) to the corresponding dual problem. This paper shows that an … Read more