On the use of piecewise linear models in nonlinear programming

Richard H. Byrd, Jorge Nocedal*, Richard A. Waltz, Yuchen Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming and sequential linear-quadratic programming methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian.

Original languageEnglish (US)
Pages (from-to)289-324
Number of pages36
JournalMathematical Programming
Issue number1-2
StatePublished - Jan 1 2013


  • 65K05
  • 90C06
  • 90C30
  • 90C55
  • Mathematics Subject Classification (2000): 49M37

ASJC Scopus subject areas

  • Mathematics(all)
  • Software


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