An interior point potential reduction method for constrained equations |
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Authors: | Tao Wang Renato D C Monteiro Jong-Shi Pang |
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Institution: | (1) Department of Mathematical Sciences, The Johns Hopkins University, 21218-2689 Baltimore, MD, USA;(2) School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205 Atlanta, GA, USA |
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Abstract: | We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton
method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs,
linear and nonlinear complementarity problems. In general, constrained equations provide a unified formulation for many mathematical
programming problems, including complementarity problems of various kinds and the Karush-Kuhn-Tucker systems of variational
inequalities and nonlinear programs. Combining ideas from the damped Newton and interior point methods, we present an iterative
algorithm for solving a constrained system of equations and investigate its convergence properties. Specialization of the
algorithm and its convergence analysis to complementarity problems of various kinds and the Karush-Kuhn-Tucker systems of
variational inequalities are discussed in detail. We also report the computational results of the implementation of the algorithm
for solving several classes of convex programs.
The work of this author was based on research supported by the National Science Foundation under grants DDM-9104078 and CCR-9213739
and the Office of Naval Research under grant N00014-93-1-0228.
The work of this author was based on research supported by the National Science Foundation under grant DMI-9496178 and the
Office of Naval Research under grants N00014-93-1-0234 and N00014-94-1-0340. |
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Keywords: | Constrained equations Interior point methods Potential reduction Complementarity problem Variational inequality Convex programs |
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