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An interior point
potential reduction method for constrained equations

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T. Wang, R.D.C. Monteiro, and J.-S. Pang

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.

Final revision: October, 1995.