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| 摘要: |
| 本文研究了一类线性约束变分不等式（VI）的幂罚函数法求解问题.利用VI的KKT条件，将VI转化为等价的混合互补问题和一个新的VI问题，并在一定条件下分析了解的存在性和唯一性.利用度理论证明了幂罚方程组解的存在性与唯一性.由以上结果最终证明了幂罚函数法的收敛性，即幂罚方程组的解收敛于VI问题的解. |
| 关键词: 变分不等式 线性约束 互补问题 幂罚函数法 |
| DOI： |
| 分类号:O224 |
| 基金项目: |
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| POWER PENALTY METHOD FOR VARIATIONAL INEQUALITY PROBLEMS WITH A CLASS OF LINEAR CONSTRAINTS |
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YANG Bo,HUANG Chong-chao
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| Abstract: |
| In this paper, we study the problem that adopts power penalty method to solve a variational inequality (VI) problem with a class of linear constraints. Under certain conditions, by using the KKT condition of the VI, we transform the VI problem into an equivalent mixed complementarity problem and a new VI problem and analyze the existence and uniqueness of the solutions. In addition, we prove the existence of solution of the power penalty equations by degree theory and the uniqueness. At last, we prove the convergence of the power penalty method, in other words, the solution of the power penalty equations converges to the solution of the VI problem. |
| Key words: variational inequality linear constraint complementarity problem power penalty method |
