New smooth gap function for box constrained variational inequalities

doi:10.1007/s10483-013-1649-x

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (1): 15-26.doi: https://doi.org/10.1007/s10483-013-1649-x

New smooth gap function for box constrained variational inequalities

张丽丽¹，李兴斯²

1. School of Mathematical Science, Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China;
2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China

收稿日期:2012-06-20 修回日期:2012-06-28 出版日期:2013-01-03 发布日期:2013-01-03
通讯作者: Xing-si LI E-mail:xingsi_li@yahoo.com.cn
基金资助:
the National Natural Science Foundation of China (Nos. 10902077, 11172209, and 10572031)

New smooth gap function for box constrained variational inequalities

Li-li ZHANG¹, Xing-si LI²

1. School of Mathematical Science, Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China;
2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China

Received:2012-06-20 Revised:2012-06-28 Online:2013-01-03 Published:2013-01-03
Contact: Xing-si LI E-mail:xingsi_li@yahoo.com.cn
Supported by:
the National Natural Science Foundation of China (Nos. 10902077, 11172209, and 10572031)

摘要/Abstract

摘要： A new smooth gap function for the box constrained variational inequality problem (VIP) is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

关键词: 1-jet bundle, dynamical flow, vertical endomorphism, connection, geodesic

Abstract: A new smooth gap function for the box constrained variational inequality problem (VIP) is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

Key words: 1-jet bundle, dynamical flow, vertical endomorphism, connection, geodesic

张丽丽;李兴斯. New smooth gap function for box constrained variational inequalities[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 15-26.

Li-li ZHANG;Xing-si LI. New smooth gap function for box constrained variational inequalities[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 15-26.

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New smooth gap function for box constrained variational inequalities

New smooth gap function for box constrained variational inequalities

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