Failure of Global Convergence for a Class of Interior Point Methods for Nonlinear Programming

Andreas Wächter (andreaswandrew.cmu.edu)
Lorenz T. Biegler (lb01andrew.cmu.edu)

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 do produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed problem.

Keywords: nonlinear optimization, interior point methods, global convergence, Newton's method

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization

Category 3: Nonlinear Optimization

Citation: Mathematical Programming 88(3), pp. 565-587, 2000

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Entry Submitted: 08/18/2000
Entry Last Modified: 10/31/2000

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