利用关联的渐进解耦求解拟变分不等式
Solving Quasi-Variational Inequalities Using the Progressive Decoupling of Linkages
浏览论文内容
中文总结 AI 辅助
本文提出关联渐进解耦算法，将拟变分不等式转化为变分不等式序列求解，证明其收敛性，并在瓦尔拉斯均衡等问题上展现优异计算性能。
中文摘要 AI 辅助
受优化与变分不等式的关联渐进解耦方法启发，我们提出一种将拟变分不等式转化为一系列变分不等式进行求解的算法。在一些正则性条件下，该方法被证明是局部收敛的；若这些条件在整个定义域内成立，则全局收敛。此外，在另一类假设下，针对具有移动集的拟变分不等式，还建立了线性速率的全局收敛性。在大规模瓦尔拉斯均衡问题（广义纳什均衡的特例）及相关文献中的部分其他实例上，该方法展现出优异的计算性能。
英文摘要
Inspired by the progressive decoupling of linkages methodology for optimization and variational inequalities, we propose an algorithm for solving quasi-variational inequalities as a sequence of variational inequalities. Our method is shown to converge locally under some regularity conditions and globally when such conditions hold throughout the entire domain. Separately, under other type of assumptions, global convergence with linear rate is also established for the class of quasi-variational inequalities said to have a moving set. Advantageous computational performance is shown for large-scale Walrasian equilibrium problems, a special case of generalized Nash equilibria, as well as for some other instances encountered in related literature.
