Computing a Celis-Dennis-Tapia Trust Region Step for Equality Constrained Optimization

Abstract

We study an approach for minimizing a convex quadratic function subject to two quadratic constraints. This problem stems from computing a trust-region step for an SQP algorithm proposed by Celis, Dennis and Tapia (1984) for equality constrained optimization. Our approach is to reformulate the problem into a univariate nonlinear equation phi(mu) = 0 where the function phi(mu) is continuous, at least piecewise differentiable and monotone. Well-established methods then can be readily applied. We also consider an extension of our approach to a class of non-convex quadratic functions and show that our approach is applicable to reduced Hessian SQP algorithms. Numerical results are presented indicating that our algorithm is reliable, robust and has the potential to be used as a building block to construct trust-region algorithms for small-sized problems in constrained optimization.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1989
Accession Number
ADA455257

Entities

People

  • Yin Zhang

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Equations
  • Heuristic Methods
  • Information Operations
  • Mathematics
  • Operations Research
  • Optimization

Fields of Study

  • Mathematics

Readers

  • Operations Research