DIMENSION REDUCING METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS AND UNCONSTRAINED OPTIMIZATION : A REVIEW

The purpose of this report is to review a new class of methods we have proposed for solving systems of nonlinear equations and optimization problems, named Dimension Reducing Methods. These methods are based on reduction to simpler one-dimensional nonlinear equations. Although these methods use reduction to simpler one, they converge quadratically, and incorporate the advantages of nonlinear SOR and Newton’s algorithms. Moreover, since they do not directly perform function evaluations, they can be applied to problems with imprecise function values.

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