| 箱式约束变分不等式的一类新光滑gap函数 |
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| 引用本文： | 张丽丽,李兴斯. 箱式约束变分不等式的一类新光滑gap函数[J]. 应用数学和力学, 2013, 34(1): 27-37. DOI: 10.3879/j.issn.1000-0887.2013.01.004 |
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| 作者姓名： | 张丽丽 李兴斯 |
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| 作者单位： | 1大连理工大学 数学科学学院,辽宁 大连 116023;1大连理工大学 工业装备结构分析国家重点实验室,辽宁 大连 116023 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 针对箱式约束变分不等式问题，利用一类积分型全局最优性条件，提出了一个新光滑gap函数．该光滑gap函数形式简单且具有较好的性质．利用该gap函数，箱式约束变分不等式可转化为等价光滑优化问题进行求解．进一步地，讨论了可保证等价光滑优化问题的任意聚点为箱式约束变分不等式问题解的条件．以一个简单的摩擦接触问题为例阐释了该方法的应用．最后，利用标准的变分不等式考题验证了方法的有效性．
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| 关 键 词： | 箱式约束变分不等式问题 光滑gap函数 积分型全局最优性条件 |
| 收稿时间： | 2012-06-20 |
New Smooth Gap Function for Box Constrained Variational Inequalities |
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| Affiliation: | 1School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China;2State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China |
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| Abstract: | A new smooth gap function for box constrained variational inequality problem was proposed based on an integral global optimality condition. The smooth gap function was simple and had some good differentiable properties. The box constrained variational inequality problem could be reformulated as a differentiable optimization problem by using the proposed smooth gap function. Conditions under which any stationary point of the optimization problem was the solution to box constrained variational inequality problem were discussed. A simple frictional contact problem was analyzed to illustrate the application of this smooth gap function. Finally, numerical experiments confirmed the good theoretical properties of the method. |
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