On Local Convergence of the Method of Alternating Projections

نویسندگان

  • Dominikus Noll
  • Aude Rondepierre
چکیده

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O(k−ρ) for some ρ ∈ (0,∞).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Transversality and Alternating Projections for Nonconvex Sets

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.

متن کامل

Convergence Analysis of Alternating Nonconvex Projections

We consider the convergence properties for alternating projection algorithm (a.k.a alternating projections) which has been widely utilized to solve many practical problems in machine learning, signal and image processing, communication and statistics since it is a gradient-free method (without requiring tuning the step size) and it usually converges fast for solving practical problems. Although...

متن کامل

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

متن کامل

Alternating projections and coupling slope

We consider the method of alternating projections for finding a point in the intersection of two possibly nonconvex closed sets. We present a local linear convergence result that makes no regularity assumptions on either set (unlike previous results), while at the same time weakening standard transversal intersection assumptions. The proof grows out of a study of the slope of a natural nonsmoot...

متن کامل

S ep 2 00 7 Local convergence for alternating and averaged nonconvex projections

The idea of a finite collection of closed sets having " strongly regular intersection " at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably " regular " (special cases being convex sets, smooth manifolds, or feasible regions...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Foundations of Computational Mathematics

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2016