Understanding the accelerated proximal point method for strongly monotone operator

Abstract

The thesis studies acceleration of the proximal point method for strongly monotone operators, based on the accelerated proximal point method for monotone operators. We introduce a variant of the accelerated proximal point method for strongly monotone operator problems. We analyze the variant by two approaches, the bilinear analysis and the performance estimation problem approach. This variant has fast convergence rate for strongly monotone operator with some appropriately chosen parameters. In the bilinear analysis, we find eigenvalues related to the convergence rate of the variant of accelerated proximal point method. In the performance estimation problem approach, we present that the variant of accelerated proximal point method achieves a linear convergence rate for some carefully chosen parameters. Also, we numerically show that the variant of accelerated proximal point method is faster than proximal point method with specific parameter setting.