Newton Methods for Large-Scale Linear Equality-Constrained Minimization

Abstract

Newton methods for large-scale minimization subject to linear equality constraints are discussed. For large-scale problems, it may be prohibitively expensive to reduce the problem to an unconstrained problem in the null space of the constraint matrix. We investigate computational schemes that enable the computation of descent directions and directions of negative curvature without the need to know the null-space matrix. The schemes are based on factorizing a sparse symmetric indefinite matrix. Three different methods are proposed for computing the desired directions. Convergence properties for the different methods are established. (kr)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1990
Accession Number
ADA222310

Entities

People

  • Anders L. Forsgren
  • Walter Murray

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Convergence
  • Curvature
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Identities
  • Linear Algebra
  • Mathematical Programming
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Theorems

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Fluid Dynamics (CFD)
  • Linear Algebra

Technology Areas

  • Space