An Euler-Newton Continuation Method for Tracking Solution Trajectories of Parametric Variational Inequalities
An Euler-Newton Continuation Method for Tracking Solution Trajectories of Parametric Variational Inequalities
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DOI：
10.1137/120876915
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发表时间：
2013-05
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影响因子：
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通讯作者：
A. Dontchev;M. Krastanov;R. Rockafellar;V. Veliov
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文献类型：
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作者：
A. Dontchev;M. Krastanov;R. Rockafellar;V. Veliov
在一般集值解映射的图的每一点都是强正则点的条件下，研究了一类以t\in [0，1]$为参数的有限维变分不等式.证明了在$[0，1]$上有许多Lipschitz连续函数，它们的图互不相交，使得对于每个参数值，解映射的值集是这些函数值的并集.此外，强正则性的性质是一致的关于参数沿着任何这样的函数图。介绍了一种跟踪解轨迹的欧拉-牛顿延拓方法，并证明了该方法具有O（h^4）阶精度，从而推广了方程的一个已知误差估计.两个参数化跟踪经济均衡的例子说明了理论结果。（附更正）
A finite-dimensional variational inequality parameterized by $t\in [0,1]$ is studied under the assumption that each point of the graph of its generally set-valued solution mapping is a point of strongly regularity. It is shown that there are finitely many Lipschitz continuous functions on $[0,1]$ whose graphs do not intersect each other such that for each value of the parameter the set of values of the solution mapping is the union of the values of these functions. Moreover, the property of strong regularity is uniform with respect to the parameter along any such function graph. An Euler--Newton continuation method for tracking a solution trajectory is introduced and demonstrated to have $l^\infty$ accuracy of order $O(h^4)$, thus generalizing a known error estimate for equations. Two examples of tracking economic equilibrium parametrically illustrate the theoretical results. (A correction is attached.)