A practical anti-cycling procedure for linearly constrained optimization

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

Research output: Contribution to journalArticle

Abstract

A procedure is described for preventing cycling in active-set methods for linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance of infeasibilities in all variables, and maintenance of a "working" feasibility tolerance that increases over a long sequence of iterations. The additional work per iteration is nominal, and "stalling" cannot occur with exact arithmetic. The method appears to be reliable, based on computational results for the first 53 linear programming problems in the Netlib set.

Original languageEnglish (US)
Pages (from-to)437-474
Number of pages38
JournalMathematical Programming
Volume45
Issue number1-3
DOIs
StatePublished - Aug 1989

Fingerprint

Constrained optimization
Cycling
Constrained Optimization
Linear programming
Linearly
Active Set Method
Iteration
Infeasibility
Simplex Method
Categorical or nominal
Tolerance
Computational Results
Maintenance
Simplex method
Acceptance

Keywords

  • active-set methods
  • cycling
  • degeneracy
  • Linear programming
  • simplex method

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research
  • Software
  • Computer Graphics and Computer-Aided Design
  • Computer Science(all)

Cite this

A practical anti-cycling procedure for linearly constrained optimization. / Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Wright, Margaret.

In: Mathematical Programming, Vol. 45, No. 1-3, 08.1989, p. 437-474.

Research output: Contribution to journalArticle

Gill, Philip E. ; Murray, Walter ; Saunders, Michael A. ; Wright, Margaret. / A practical anti-cycling procedure for linearly constrained optimization. In: Mathematical Programming. 1989 ; Vol. 45, No. 1-3. pp. 437-474.
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