Local Behavior of the Newton Method on Two Equivalent Systems from Linear Programming

C. Villalobos, R. Tapia and Y. Zhang
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C. Villalobos: University of Texas at El Paso
R. Tapia: Rice University
Y. Zhang: Rice University

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 2, No 1, 239-263

Abstract: Abstract Newton's method is a fundamental technique underlying many numerical methods for solving systems of nonlinear equations and optimization problems. However, it is often not fully appreciated that Newton's method can produce significantly different behavior when applied to equivalent systems, i.e., problems with the same solution but different mathematical formulations. In this paper, we investigate differences in the local behavior of Newton's method when applied to two different but equivalent systems from linear programming: the optimality conditions of the logarithmic barrier function formulation and the equations in the so-called perturbed optimality conditions. Through theoretical analysis and numerical results, we provide an explanation of why Newton's method performs more effectively on the latter system.

Keywords: Newton's method; equivalent systems; sphere of convergence; linear programming (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1013665605315

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