New fast proximal point algorithms for monotone inclusion problems with applications to image recovery

Abstract

The proximal point algorithm has many applications for convex optimization with several versions of the proximal point algorithm including generalized proximal point algorithms and accelerated proximal point algorithms that have been studied in the literature. In this paper, we propose accelerated versions of generalized proximal point algorithms to find a zero of a maximal monotone operator in Hilbert spaces. We give both weak and linear convergence results of our proposed algorithms under standard conditions. Numerical applications of our results to image recovery are given and numerical implementations show that our algorithms are effective and superior to other related accelerated proximal point algorithms in the literature.

Keywords:

• Accelerated proximal point algorithm
• maximal monotone operators
• weak & linear convergence
• image recovery

2010 Mathematics Subject Classifications:

• 90C25
• 90C60
• 68Q25
• 49M25
• 90C22

Disclosure statement

No potential conflict of interest was reported by the author(s).