【摘要】 建立变分不等式问题KKT条件与光滑带约束方程组的等价关系,进而转化为约束优化问题。利用Levenberg-Marquardt方法给出求解变分不等式问题的算法,在不要求梯度矩阵非奇异的条件下得到了算法的全局收敛性。该算法在一定条件下是局部超线性或二次收敛的。更多还原

【Abstract】 Variational inequality is a very important field in applied mathematics and it is a key problem to obtain its solution efficiently and rapidly.The equivalent relation of variational inequality problem KKT conditions and smooth equations with constraint is first obtained,and then it is transformed to a constrained optimal problem,which can be solved by using the corresponding Levenberg-Marquardt algorithm.Under the condition without gradient matrix nonsingular,it is shown that the algorithm is global convergent.The algorithm is local super-linear convergent or quadratically convergent under the appropriate condition.更多还原