A Unified Approach to Global Convergence of Trust-Region Methods for Nonsmooth Optimization

Abstract

This paper investigates the global convergence of trust region (TR) methods for solving nonsmooth minimization problems. For a class of nonsmooth objective functions called regular functions, conditions are found on the TR local models that imply three fundamental convergence properties. These conditions are shown to be satisfied by appropriate forms of Fletcher's TR method for solving constrained optimization problems, Powell and Yuan's TR method for solving nonlinear fitting problems, Zhang, Kim and Lasdon's successive linear programming method for solving constrained problems, Duff, Nocedal and Reid's TR method for solving systems of nonlinear equations, and El Hallabi and Tapia's TR method for solving systems of nonlinear equations. Thus our results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1993
Accession Number
ADA455260

Entities

People

  • John E. Dennis
  • Richard A. Tapia
  • Shou-bai B. Li

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Convergence
  • Equations
  • Information Operations
  • Linear Programming
  • Mathematics
  • Military Research
  • Optimization

Fields of Study

  • Mathematics

Readers

  • Materials Science.
  • Operations Research