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

Andreas Wächter; Lorenz T. Biegler

doi:10.1007/PL00011386

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

Andreas Wächter^*, Lorenz T. Biegler

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

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.

Original language	English (US)
Pages (from-to)	565-574
Number of pages	10
Journal	Mathematical Programming, Series B
Volume	88
Issue number	3
DOIs	https://doi.org/10.1007/PL00011386
State	Published - Jan 1 2000

Keywords

Global convergence
Interior point methods
Newton's method
Nonlinear optimization

ASJC Scopus subject areas

Software
General Mathematics

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10.1007/PL00011386

Cite this

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title = "Failure of global convergence for a class of interior point methods for nonlinear programming",

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.",

keywords = "Global convergence, Interior point methods, Newton's method, Nonlinear optimization",

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year = "2000",

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AU - Biegler, Lorenz T.

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N2 - 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.

AB - 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.

KW - Global convergence

KW - Interior point methods

KW - Newton's method

KW - Nonlinear optimization

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

Abstract

Keywords

ASJC Scopus subject areas

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