Journal ArticleDOI
On the Convergence of Sequences of Convex Sets in Finite Dimensions
G. Salinetti,Roger J.-B. Wets +1 more
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In this article, four types of convergence for sequences of convex sets are investigated and their interrelationships are explored for convex sequences of sets with respect to convex set sets.Abstract:
Four types of convergence for sequences of convex sets are investigated Their interrelationships are exploredread more
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Convex bodies : the Brunn-Minkowski theory
TL;DR: Inequalities for mixed volumes 7. Selected applications Appendix as discussed by the authors ] is a survey of mixed volumes with bounding boxes and quermass integrals, as well as a discussion of their applications.
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Convergence theorems for Banach space valued integrable multifunctions.
TL;DR: In this article, the authors generalize a result of Kato on the pointwise behavior of a P weakly convergent sequence in the Lebesgue-Bochner spaces LX(fi) (I < p < (R)) to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions.
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Quantitative stability of variational systems. I. The epigraphical distance
Hedy Attouch,Roger J.-B. Wets +1 more
TL;DR: In this article, a global measure for the distance between the elements of a variational system (parametrized families of optimization problems) is proposed, where the distance is defined as the distance from the elements to the optimizer.
Journal ArticleDOI
Computational Design of Sequences With Good Correlation Properties
Mojtaba Soltanalian,Petre Stoica +1 more
TL;DR: A computational framework based on an iterative twisted approximation (ITROX) and a set of associated algorithms for various sequence design problems and a modified version of the general framework that can be useful in constrained alphabets are introduced.
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On the Convergence in Distribution of Measurable Multifunctions Random Sets Normal Integrands, Stochastic Processes and Stochastic Infima
G. Salinetti,Roger J.-B. Wets +1 more
TL;DR: In this paper, the concept of the distribution function of a closed-valued measurable multifunction is introduced and used to study the convergence of sequences of multifunctions and the epi-convergence in distribution of normal integrands and stochastic processes; in particular various compactness criteria are exhibited.
References
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Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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Convergence of convex sets and of solutions of variational inequalities
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Sur la fonction d’appui des ensembles convexes dans un espace localement convexe
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On the continuity of the minimum set of a continuous function
TL;DR: In this article, necessary and sufficient conditions for the solution of a constrained minimization problem will vary continuously when the constraints and objective function are varied, and special results for the case that the constraints are linear inequalities.