Abstract

This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that heuristic adaptive choices, such as Mehrotra's probing procedure, outperform monotone strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the minimization of a quality function. The paper also proposes a globalization framework that ensures the convergence of adaptive interior methods, and examines convergence failures of the Mehrotra predictor-corrector algorithm. The barrier update strategies proposed in this paper are applicable to a wide class of interior methods and are tested in the two distinct algorithmic frameworks provided by the ipopt and knitro software packages.

MSC codes

  1. 49M37
  2. 65K05
  3. 90C06
  4. 90C30
  5. 90C51

Keywords

  1. interior-point methods
  2. barrier methods
  3. nonlinear programming
  4. constrained optimization

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Information & Authors

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Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 1674 - 1693
ISSN (online): 1095-7189

History

Submitted: 9 January 2006
Accepted: 12 August 2008
Published online: 28 January 2009

MSC codes

  1. 49M37
  2. 65K05
  3. 90C06
  4. 90C30
  5. 90C51

Keywords

  1. interior-point methods
  2. barrier methods
  3. nonlinear programming
  4. constrained optimization

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