128 research outputs found
Improved Bounds on Restricted Isometry Constants for Gaussian Matrices
The Restricted Isometry Constants (RIC) of a matrix measures how close to
an isometry is the action of on vectors with few nonzero entries, measured
in the norm. Specifically, the upper and lower RIC of a matrix of
size is the maximum and the minimum deviation from unity (one) of
the largest and smallest, respectively, square of singular values of all
matrices formed by taking columns from . Calculation of
the RIC is intractable for most matrices due to its combinatorial nature;
however, many random matrices typically have bounded RIC in some range of
problem sizes . We provide the best known bound on the RIC for
Gaussian matrices, which is also the smallest known bound on the RIC for any
large rectangular matrix. Improvements over prior bounds are achieved by
exploiting similarity of singular values for matrices which share a substantial
number of columns.Comment: 16 pages, 8 figure
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Multi-store Competition: Market Segmentation or Interlacing
This paper develops a model for multi-store competition between firms. Using the fact that different firms have different outlets and produce horizontally differentiated goods, we obtain a pure strategy equilibrium where firms choose a different location for each outlet and firms' locations are interlaced. The location decisions of multi-store firms are completely independent of each other. Firms choose locations that minimize transportation costs of consumers. Moreover, generically, the subgame perfect equilibrium is unique and when the firms have an equal number of outlets, prices are independent of the number of outlets
SIMULATING KNOWLEDGE-GENERATION AND DISTRIBUTION PROCESSES IN INNOVATION COLLABORATIONS AND NETWORKS
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