On gap functions for quasi-variational inequalities
On gap functions for quasi-variational inequalities
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DOI：
10.1155/2008/531361
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发表时间：
2008-01-01
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通讯作者：
Taji, Kouichi
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文献类型：
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作者：
Taji, Kouichi
对于变分不等式，人们提出了各种价值函数，如差距函数、正则化间隙函数、D-间隙函数等。这些功能导致等价的优化配方，并用于优化为基础的方法求解变分不等式。本文推广了一个拟变分不等式的正则间隙函数和D-间隙函数，它是变分不等式的推广，并用于构造广义平衡问题.这些扩展拟变分不等式制定等价的优化问题，并证明是连续的和方向可微的。Copyright（c）2008.
For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable. Copyright (c) 2008.