Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/7914
Title: A box-constrained differentiable penalty method for nonlinear complementarity problems
Authors: Tian, B
Hu, Y
Yang, X 
Keywords: Convergence rate
Differentiable penalty method
Least squares method
Nonlinear complementarity problem
ℓ1p-penalty method
Issue Date: 2015
Publisher: Springer
Source: Journal of global optimization, 2015, v. 62, no. 4, p. 729-747 How to cite?
Journal: Journal of global optimization 
Abstract: In this paper, we propose a box-constrained differentiable penalty method for nonlinear complementarity problems, which not only inherits the same convergence rate as the existing $$\ell _\frac{1}{p}$$ℓ1p-penalty method but also overcomes its disadvantage of non-Lipschitzianness. We introduce the concept of a uniform $$\xi $$ξ–$$P$$P-function with $$\xi \in (1,2]$$ξ∈(1,2], and apply it to prove that the solution of box-constrained penalized equations converges to that of the original problem at an exponential order. Instead of solving the box-constrained penalized equations directly, we solve a corresponding differentiable least squares problem by using a trust-region Gauss–Newton method. Furthermore, we establish the connection between the local solution of the least squares problem and that of the original problem under mild conditions. We carry out the numerical experiments on the test problems from MCPLIB, and show that the proposed method is efficient and robust.
URI: http://hdl.handle.net/10397/7914
ISSN: 0925-5001
EISSN: 1573-2916
DOI: 10.1007/s10898-015-0275-6
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