A Power Penalty Method for box constrained variational inequality Problem

DOI

10.2991/meic-14.2014.187How to use a DOI?

Keywords

box constrained variational inequality; nonlinear mixed complementarity; power penalty method; monotone; Holder continuous

Abstract

The variational inequality and the nonlinear complementarity problems has been well documented in the literature.Many methods such as nonsmooth Newton method and interior point method were studied in the variational inequality problem,but there was a limited study of penalty methods for the variational inequality problem.And a power penalty methods was presented for the box variational inequality problem in this paper.The box constrained variational inequality problem first was proved to be equivalent to a nonlinear mixed complementarity problem and a new variational inequality problem , and present a novel power penalty approach to the new variational inequality problem in which the variational inequality problem is approximated by a nonlinear equation containing a power term. We show that the solution to the penalty equation converges to that of the VIP in the Euclidean norm when the function involved is Holder continuous and has a certain monotonicity property. Finally, we use  a 3-dimensional vector-valued function defined to demonstrate the effectiveness of the algorithm.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xizhen Hu
AU  - Yang Yang
AU  - Sihong Liao
AU  - Xiaobei Hu
PY  - 2014/11
DA  - 2014/11
TI  - A Power Penalty Method for box constrained variational inequality Problem
BT  - Proceedings of the 2014 International Conference on Mechatronics, Electronic, Industrial and Control Engineering
PB  - Atlantis Press
SP  - 835
EP  - 838
SN  - 2352-5401
UR  - https://doi.org/10.2991/meic-14.2014.187
DO  - 10.2991/meic-14.2014.187
ID  - Hu2014/11
ER  -