A Global and Local Superlinear Continuation-Smoothing Method for P0 and R0 NCP or Monotone NCP

Authors:
Bintong Chen;Xiaojun Chen
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
1999

Citing 0
Cited 14

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A Smoothing Newton Method for General Nonlinear Complementarity Problems

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A New Path-Following Algorithm for Nonlinear P*Complementarity Problems

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Smoothing-type algorithm for solving linear programs by using an augmented complementarity problem

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A smoothing-type algorithm for solving system of inequalities

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A variant smoothing Newton method for P0-NCP based on a new smoothing function

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A non-interior continuation algorithm for the CP based on a generalized smoothing function

Journal of Computational and Applied Mathematics
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones

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Sufficient conditions on nonemptiness and boundedness of the solution set of the P0 function nonlinear complementarity problem

Operations Research Letters

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Abstract

We propose a continuation method for a class of nonlinear complementarity problems (NCPs), including the NCP with a P0 and R0 function and the monotone NCP with a feasible interior point. The continuation method is based on a class of Chen--Mangasarian smoothing functions. Unlike many existing continuation methods, the method follows noninterior smoothing paths, and, as a result, initial points can be easily constructed. In addition, we introduce a procedure to dynamically update the neighborhoods associated with the smoothing paths, so that the algorithm is both globally convergent and locally superlinearly convergent under suitable assumptions. Finally, a hybrid continuation-smoothing method is proposed and is shown to have the same convergence properties under weaker conditions.