Comparison of two sets of first-order conditions as bases of interior-point Newton methods for optimization with simple bounds

In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions was proposed by Coleman and Li; the other is the standard KKT set of condition...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2002-04, Vol.113 (1), p.21-40
Main Authors: JAMROG, D. C, TAPIA, R. A, ZHANG, Y
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Applied sciences
Exact sciences and technology
Lagrange multiplier
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Optimization. Search problems
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Summary:In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions was proposed by Coleman and Li; the other is the standard KKT set of conditions. We discuss a perturbation of the CL conditions for problems with one-sided bounds and the difficulties involved in extending this to problems with general bounds. We study the numerical behavior of the Newton method applied to the systems of equations associated with the unperturbed and perturbed necessary conditions. Preliminary numerical results for convex quadratic objective functions indicate that, for this class of problems, the Newton method based on the perturbed KKT formulation appears to be the more robust.
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1014801112646