Procedures for optimization problems with a mixture of bounds and general linear constraints

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

Research output: Contribution to journalArticlepeer-review


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 constraints 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. In this paper, we 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 (TOMS)
Issue number3
StatePublished - Aug 28 1984


  • Active-set methods
  • Cholesky factorlzation
  • TQ factorization
  • bound constraints
  • linear constraints
  • updating matrix factorizations

ASJC Scopus subject areas

  • Software
  • Applied Mathematics


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