Composition duality and maximal monotonicity
Composition duality and maximal monotonicity
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DOI：
10.1007/s101070050043
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发表时间：
1999-05
影响因子：
2.7
通讯作者：
S. M. Robinson
中科院分区：
文献类型：
--
作者：
S. M. Robinson
抽象。本文证明了算子包含的Attouch-Thera对偶原理如何推广到多函数的复合，使得原包含和对偶包含可以包含不同空间对之间的算子.我们首先介绍了扩展，并给出了一个计算经济学的例子来证明它具有实用价值。然后我们考虑应用中经常出现的一种特殊情况，涉及真实的Hilbert空间和极大单调算子。我们表明，在这种情况下，我们的二元性框架包括以前开发的Rockafellar，Mosco和Gabay。最后，我们证明，在这种情况下，在非常简单的假设下的对偶变换保持最大单调性的运营商参与。本文证明了L [sup*] TL型算子的极大单调性，其中T是极大单调的，L是线性连续的，且伴随L [sup*]。
Abstract. This paper shows how the Attouch-Thera duality principle for operator inclusions can be extended to compositions of multifunctions, so that the primal and dual inclusions may involve operators between different pairs of spaces. We first present the extension and give an example from computational economics to demonstrate that it has practical utility. Then we consider a particular case, often found in applications, involving real Hilbert spaces and maximal monotone operators. We show that in this case our duality framework includes those previously developed by Rockafellar, Mosco, and Gabay. Finally we demonstrate that in this case, under very simple hypotheses the duality transformation preserves the maximal monotonicity of the operators involved. This proof uses an apparently new criterion for maximal monotonicity of operators of the form L [sup*] TL, where T is maximal monotone and L is linear and continuous with adjoint L [sup*].