Sufficient Conditions for Error Bounds and Applications
Sufficient Conditions for Error Bounds and Applications
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DOI：
10.1007/s00245-004-0799-5
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发表时间：
2004-07
影响因子：
1.8
通讯作者：
P. Bosch;A. Jourani;R. Henrion
中科院分区：
文献类型：
--
作者：
P. Bosch;A. Jourani;R. Henrion
本文的目的是给出一般Banach空间中Fréchet次微分和极限Fréchet次微分的误差界的充分条件。这使我们能够发展形式为（x，y）∈ C × D，g（x，y，u）= 0的系统的近似次微分的充分条件，其中g在无限维空间中取值，u起参数的作用。这种对称结构为我们提供了对C或D施加条件的选择。利用这些结果证明了Fritz-John和Karush-Kuhn-Tucker乘子集的非空性和弱星紧性，建立了值函数的Lipschitz连续性并计算了其次微分，最后得到了非凸无界微分包含控制问题的局部能控性结果.
Our aim in this paper is to present sufficient conditions for error bounds in terms of Fréchet and limiting Fréchet subdifferentials in general Banach spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (x, y) ∈ C × D, g(x, y, u) = 0, where g takes values in an infinite-dimensional space and u plays the role of a parameter. This symmetric structure offers us the choice of imposing conditions either on C or D. We use these results to prove the nonemptiness and weak-star compactness of Fritz–John and Karush–Kuhn–Tucker multiplier sets, to establish the Lipschitz continuity of the value function and to compute its subdifferential and finally to obtain results on local controllability in control problems of nonconvex unbounded differential inclusions.