Optimization Online


Convergence of a hybrid projection-proximal point algorithm coupled with approximation methods in convex optimization

Felipe Alvarez (falvarez***at***dim.uchile.cl)
Miguel Carrasco (migucarr***at***dim.uchile.cl)
Karine Pichard (kpichard***at***dim.uchile.cl)

Abstract: In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a generic diagonal hybrid algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis is valid for nonsmooth data in infinite-dimensional Hilbert spaces. Some examples are presented, in particular some penalty/barrier methods in convex programming. We also show that some results can be adapted to the zero-finding problem for a maximal monotone operator.

Keywords: Parametric approximation; diagonal iteration; proximal point; hybrid method ; global convergence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Global Optimization (Other )

Citation: Mathematics of Operations Research Vol. 30, No. 4, November 2005, pp. 966-984


Entry Submitted: 11/03/2004
Entry Accepted: 11/03/2004
Entry Last Modified: 02/28/2006

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society