Newton's method for B-differentiable equations
Mathematics of Operations Research
Newton's method for the nonlinear complementarity problem: a B-differentiable equation problem
Mathematical Programming: Series A and B
NE/SQP: a robust algorithm for the nonlinear complementarity problem
Mathematical Programming: Series A and B
Global convergence of damped Newton's method for nonsmooth equations via the path search
Mathematics of Operations Research
Inexact Newton methods for solving nonsmooth equations
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
QPCOMP: a quadratic programming based solver for mixed complementarity problems
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Smooth Approximations to Nonlinear Complementarity Problems
SIAM Journal on Optimization
Existence and Limiting Behavior of Trajectories Associatedwith P0-equations
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Computational Optimization and Applications
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In this paper, we describe a new, integral-based smoothing methodfor solving the mixed nonlinear complementarity problem (MNCP). Thisapproach is based on recasting MNCP as finding the zero of a nonsmoothsystem and then generating iterates via two types of smooth approximationsto this system. Under weak regularity conditions, we establish that thesequence of iterates converges to a solution if the limit point of thissequence is regular. In addition, we show that the rate is Q-linear,Q-superlinear, or Q-quadratic depending on the level of inexactness in thesubproblem calculations and we make use of the inexact Newton theory ofDembo, Eisenstat, and Steihaug. Lastly, we demonstrate the viability of theproposed method by presenting the results of numerical tests on a variety ofcomplementarity problems.