Linearly convergent inexact proximal point algorithm for minimization. Revision 1

PDF Version Also Available for Download.

Description

In this paper, we propose a linearly convergent inexact PPA for minimization, where the inner loop stops when the relative reduction on the residue (defined as the objective value minus the optimal value) of the inner loop subproblem meets some preassigned constant. This inner loop stopping criterion can be achieved in a fixed number of iterations if the inner loop algorithm has a linear rate on the regularized subproblems. Therefore the algorithm is able to avoid the computationally expensive process of solving the inner loop subproblems exactly or asymptotically accurately; a process required by most of the other linearly convergent ... continued below

Physical Description

28 p.

Creation Information

Zhu, C. August 1, 1993.

Context

This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Author

Sponsors

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

Description

In this paper, we propose a linearly convergent inexact PPA for minimization, where the inner loop stops when the relative reduction on the residue (defined as the objective value minus the optimal value) of the inner loop subproblem meets some preassigned constant. This inner loop stopping criterion can be achieved in a fixed number of iterations if the inner loop algorithm has a linear rate on the regularized subproblems. Therefore the algorithm is able to avoid the computationally expensive process of solving the inner loop subproblems exactly or asymptotically accurately; a process required by most of the other linearly convergent PPAs. As applications of this inexact PPA, we develop linearly convergent iteration schemes for minimizing functions with singular Hessian matrices, and for solving hemiquadratic extended linear-quadratic programming problems. We also prove that Correa-Lemarechal`s ``implementable form`` of PPA converges linearly under mild conditions.

Physical Description

28 p.

Notes

OSTI as DE96007636

Source

  • Other Information: PBD: Aug 1993

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • Other: DE96007636
  • Report No.: MCS--P385-0993-Rev.1
  • Grant Number: W-31109-ENG-38
  • DOI: 10.2172/205211 | External Link
  • Office of Scientific & Technical Information Report Number: 205211
  • Archival Resource Key: ark:/67531/metadc670949

Collections

This report is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this report?

When

Dates and time periods associated with this report.

Creation Date

  • August 1, 1993

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

Description Last Updated

  • Aug. 23, 2016, 3:09 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 3

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Zhu, C. Linearly convergent inexact proximal point algorithm for minimization. Revision 1, report, August 1, 1993; Illinois. (digital.library.unt.edu/ark:/67531/metadc670949/: accessed November 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.