An inexact Newton method for nonconvex equality constrained optimization

Richard H. Byrd, Frank E. Curtis, Jorge Nocedal

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351-369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.

Original languageEnglish (US)
Pages (from-to)273-299
Number of pages27
JournalMathematical Programming
Issue number2
StatePublished - Apr 2010


  • Constrained optimization
  • Inexact linear system solvers
  • Krylov subspace methods
  • Large-scale optimization
  • Nonconvex programming

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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