拟变分不等式的求解及分解算法

Most of problems in Mathematical Programming and Operations Research can be converted to a variational inequality. Numerical methods for variational inequality problems is a challenging and attractive research field in both applied and numerical mathematics. In this project, we study numerical methods for a class of quasi-variational inequalities (variational inequality whose constraint set is dependent on the variables) and the decomposition methods for structured.variational inequalities. For quasi-variational inequalities, we translate them to a general variational inequality and propose a class of inexact implicit methods. Since the efficiency of the original alternating direction methods is signicicatly dependent on some penalty and proximal parameters, we develope some self-adaptive techniques for the decomposition methods..Theoretically, we prove the convergence of the methods with variable parameters, and in numerical experients, we demonstrate the effectiveness and necessarty of the self-adaptivetechniques

变分不等式是数学规划中一类有广泛应用和相当难度的问题。本项目研究内容之一是求解更一般的约束集合依赖于变量的拟变分不等式。另一项内容是开发一类新的分解算法（交替方向法），与通常的方法不同，它在每步迭代中需要求解的不再是一个与原问题难度相同而皇枪婺Ｂ孕〉姆窍咝员浞植坏仁剑鞘砑庵杏谐墒烊砑蠼獾摹傲夹?”子问题。