Journal of Optimization Theory and Applications

, Volume 26, Issue 4, pp 485–500 | Cite as

Local convergence of the diagonalized method of multipliers

  • R. H. Byrd
Contributed Papers

Abstract

In this study, we consider a modification of the method of multipliers of Hestenes and Powell in which the iteration is diagonalized, that is, only a fixed finite number of iterations of Newton's method are taken in the primal minimization stage. Conditions are obtained for quadratic convergence of the standard method, and it is shown that a diagonalization where two Newton steps are taken preserves the quadratic convergence for all multipler update formulas satisfying these conditions.

Key Words

Newton-Raphson method nonlinear programming method of multipliers augmented Lagrangian method 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • R. H. Byrd
    • 1
  1. 1.Department of Mathematical SciencesThe Johns Hopkins UniversityBaltimore

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