排序方式: 共有13条查询结果,搜索用时 15 毫秒
1.
Well-Posedness by Perturbations of Variational Problems 总被引:3,自引:0,他引:3
Lemaire B. Ould Ahmed Salem C. Revalski J. P. 《Journal of Optimization Theory and Applications》2002,115(2):345-368
In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented. 相似文献
2.
Robert Deville Julian P. Revalski 《Proceedings of the American Mathematical Society》2000,128(4):1117-1124
We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.
3.
Teemu Pennanen Julian P. Revalski Michel Thé ra 《Proceedings of the American Mathematical Society》2003,131(12):3721-3729
In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uniformly locally bounded around any point from the interior of the domain of the limit mapping. The result is an extension of a similar one from finite dimensions. As an application we give a simplified condition for the stability (under graph-distance convergence) of the sum of maximal monotone mappings in Hilbert spaces.
4.
Alwadani Salihah Bauschke Heinz H. Revalski Julian P. Wang Xianfu 《Set-Valued and Variational Analysis》2021,29(3):721-733
Set-Valued and Variational Analysis - Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices... 相似文献
5.
Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of continuous minimization problems coincide is given. It is shown that the equivalence between the original Tikhonov well-posedness and the ones above provides a new characterization of the so-called Atsuji spaces. Generalized notions of well-posedness, not requiring uniqueness of the solution, are introduced and investigated in the above spirit. 相似文献
6.
We study generic variational principles in optimization when the underlying topological space X is not necessarily metrizable. It turns out that, to ensure the validity of such a principle, instead of having a complete metric which generates the topology in the space X (which is the case of most variational principles), it is enough that we dispose of a complete metric on X which is stronger than the topology in X and fragments the space X. 相似文献
7.
This paper proposes a regularized notion of a composition of a monotone operator with a linear mapping. This new concept, called variational composition, can be shown to be maximal monotone in many cases where the usual composition is not. The two notions coincide, however, whenever the latter is maximal monotone. The utility of the variational composition is demonstrated by applications to subdifferential calculus, theory of measurable multifunctions, and elliptic PDEs with singular coefficients. 相似文献
8.
Marc Lassonde Julian P. Revalski 《Proceedings of the American Mathematical Society》2005,133(9):2637-2646
We propose to study fragmentability of set-valued mappings not only for a given single mapping, but also for a sequence of mappings associated with the initial one. It turns out that this property underlies several variational principles, such as for example the Deville-Godefroy-Zizler variational principle and the Stegall variational principle, by providing a common path for proof.
9.
The existence of special kind of winning strategies in the Banach-Mazur game in a completely regular topological spaceX is shown to be equivalent to generic stability properties of optimization problems generated by the continuous bounded real-valued functions inX.Research partially supported by the National Foundation for Scientific Research at the Bulgarian Ministry of Education and Science under Grant Number MM-408/94. 相似文献
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