Mathematical Programming

, Volume 88, Issue 3, pp 565–574 | Cite as

Failure of global convergence for a class of interior point methods for nonlinear programming

  • Andreas Wächter
  • Lorenz T. Biegler

Abstract.

Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed problem.

Key words: nonlinear optimization – interior point methods – global convergence – Newton’s method 
Mathematics Subject Classification (1991): 65K05, 90G30, 90G51 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andreas Wächter
    • 1
  • Lorenz T. Biegler
    • 1
  1. 1.Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA, e-mail: {andreasw, lb01}@andrew.cmu.eduUS

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