- Inexact and accelerated proximal point algorithms Saverio Salzo (salzodisi.unige.it) Silvia Villa (villadima.unige.it) Abstract: We present inexact accelerated proximal point algorithms for minimizing a proper lower semicon- tinuous and convex function. We carry on a convergence analysis under different types of errors in the evaluation of the proximity operator, and we provide corresponding convergence rates for the objective function values. The proof relies on a generalization of the strategy proposed in [O. Güler. New proximal point algorithms for convex minimization. SIAM J. on Optimization, 2(4):649–664, 1992] for generating estimate sequences according to the definition of Nesterov, and is based on the concept of $\epsilon$-subdifferential. We show that the convergence rate of the exact accelerated algorithm $1/k^2$ can be recovered by constraining the errors to be of a certain type. Keywords: accelerated proximal point algorithms, global convergence rates, approximation criteria Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF]Entry Submitted: 08/10/2011Entry Accepted: 08/10/2011Entry Last Modified: 08/17/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.