Some Theoretical Properties of an Augmented Lagrangian Merit Function.

Abstract

Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate variable, and inequality constraints are handled by means of non-negative slack variables that are included in the linesearch. Global convergence is proved for an SQP algorithm that uses his merit function. We also prove that steps of unity are accepted in a neighborhood of the solution when this merit function is used in a suitable superlinearly convergent algorithm. Finally, a selection of numerical results is presented to illustrate the performance of the associated SQP method. Keywords: Sequential Quadratic Programming.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1986
Accession Number
ADA168503

Entities

People

  • Margaret H. Wright
  • Michael Saunders
  • Philip Edward Gill
  • Walter Murray

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computer Programming
  • Contracts
  • Convergence
  • Inequalities
  • Iterations
  • Lagrangian Functions
  • Mathematical Programming
  • Military Research
  • New York
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Systems Science

Fields of Study

  • Mathematics

Readers

  • Operations Research