A posteriori error bounds for the linearly-constrained varitional inequality problem
Mathematics of Operations Research
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Growth behavior of a class of merit functions for the nonlinear complementarity problem
Journal of Optimization Theory 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
Beyond Monotonicity in Regularization Methods for Nonlinear Complementarity Problems
SIAM Journal on Control and Optimization
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Modified Wilson'S Method for Nonlinear Programswith Nonunique Multipliers
Mathematics of Operations Research
SIAM Journal on Optimization
On the Identification of Zero Variables in an Interior-Point Framework
SIAM Journal on Optimization
On the convergence of an inexact Newton-type method
Operations Research Letters
| Hi-index | 0.00 |
The purpose of this paper is to present an algorithm for solving the monotone nonlinear complementarity problem (NCP) that enjoys superlinear convergence in a genuine sense without the uniqueness and nondegeneracy conditions. Recently, Yamashita and Fukushima (2001) proposed a method based on the proximal point algorithm (PPA) for monotone NCP. The method has the favorable property that a generated sequence converges to the solution set of NCP superlinearly. However, when a generated sequence converges to a degenerate solution, the subproblems may become computationally expensive and the method does not have genuine superlinear convergence. More recently, Yamashita et al. (2001) presented a technique to identify whether a solution is degenerate or not. Using this technique, we construct a differentiable system of nonlinear equations in which the solution is a solution of the original NCP. Moreover, we propose a hybrid algorithm that is based on the PPA and uses this system. We show that the proposed algorithm has a genuine quadratic or superlinear rate of convergence even if it converges to a solution that is neither unique nor nondegenerate.