A Global Convergence Theory for a Class of Trust Region Algorithms for Constrained Optimization

Abstract

This research presents a trust region algorithm for solving the equality constrained optimization problem. This algorithm is a variant of the 1984 Celis-Dennis-Tapia algorithm. The augmented Lagrangian function is used as a merit function. A scheme for updating the penalty parameter is presented. The behavior of the penalty parameter is discussed. We present a global and local convergence analysis for this algorithm. We also show that under mild assumptions, in a neighborhood of the minimizer, the algorithm will reduce to the standard SQP algorithm; hence the local rate of convergence of SQP is maintained. Our global convergence theory is sufficiently general that it holds for any algorithm that generates steps that give at least a fraction of Cauchy decrease in the quadratic model of the constraints.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1988
Accession Number
ADA455250

Entities

People

  • Mahmoud M. El-alem

Organizations

  • Rice University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Convergence
  • Evolutionary Algorithms
  • Heuristic Methods
  • Information Operations
  • Lagrangian Functions
  • Mathematics
  • Operations Research
  • Optimization
  • Standards

Readers

  • Operations Research