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作者：Luke, D. Russell; Thao, Nguyen H.; Tama, Matthew K.
作者单位：University of Gottingen; Delft University of Technology
摘要：We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity-or inverse calmness-of the mapping a...
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作者：Gillis, Nicolas; Vavasis, Stephen A.
作者单位：University of Mons; University of Waterloo
摘要：The low-rank matrix approximation problem with respect to the component-wise l(1)-norm (l(1)-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine learning. Robust PCA aims to recover a low-rank matrix that was perturbed with sparse noise, with applications for example in foreground-background video separation. Although l(1)-LRA is strongly believed to be NP-hard, there is, to our knowledge, no formal proof of thi...
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作者：Chen, Yiwei; Farias, Vivek F.
作者单位：University System of Ohio; University of Cincinnati; Massachusetts Institute of Technology (MIT)
摘要：We consider the canonical revenue management (RM) problem wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical models in RM, we assume that customers are forward looking. In particular, customers arrive randomly over time and strategize about their times of purchases. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rates of decay and these monitoring co...
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作者：Bolte, Jerome; Sabach, Shoham; Teboulle, Marc
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Technion Israel Institute of Technology; Tel Aviv University
摘要：We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in modern disparate fields of applications. It features complex geometries, qualification conditions, and other regularity properties do not hold everywhere. To address these issues, we work along several research lines to develop an original general Lagrangian m...
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作者：Gadat, Sebastien; Gavra, Ioana; Risser, Laurent
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Discrete structures like graphs make it possible to naturally and flexibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical analysis or representation problems. In this work, we develop a stochastic algorithm for finding the Fr...
