PROCEDURES FOR OPTIMIZATION PROBLEMS WITH A MIXTURE OF BOUNDS AND GENERAL LINEAR CONSTRAINTS.

Philip E. Gill, Walter Murray, Michael A. Saunders, Margaret Wright

Research output: Contribution to journalArticle

Abstract

When describing active-set methods for linearly constrained optimization, it is often convenient to treat all constraints in a uniform manner. However, in many problems the linear constants include simple bounds on the variables as well as general constraints. Special treatment of bound constraints in the implementation of a null-space active-set method yields significant advantages in computational effort and storage requirements. The authors describe a particular implementation of the constraint-related steps of a null-space active-set method when the constraint matrix is dense and bounds are treated separately. These steps involve updates to the TQ factorization of the working set of constraints and the Cholesky factorization of the projected Hessian (or Hessian approximation).

Original languageEnglish (US)
Pages (from-to)282-298
Number of pages17
JournalACM Transactions on Mathematical Software
Volume10
Issue number3
DOIs
StatePublished - Sep 1984

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Linear Constraints
Factorization
Active Set Method
Optimization Problem
Constrained optimization
Null Space
Bound Constraints
Cholesky factorisation
Constrained Optimization
Linearly
Update
Requirements
Approximation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

PROCEDURES FOR OPTIMIZATION PROBLEMS WITH A MIXTURE OF BOUNDS AND GENERAL LINEAR CONSTRAINTS. / Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Wright, Margaret.

In: ACM Transactions on Mathematical Software, Vol. 10, No. 3, 09.1984, p. 282-298.

Research output: Contribution to journalArticle

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