New smooth gap function for box constrained variational inequalities  

作　　者：张丽丽 李兴斯 

机构地区：[1]School of Mathematical Science,Dalian University of Technology [2]State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第1期15-26,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10902077,11172209, and 10572031)

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.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：box constrained variational inequality problem （VIP） smooth gap function integral global optimality condition 

分 类 号：O224[理学—运筹学与控制论] O302[理学—数学]