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作者：Arapostathis, Ari; Pang, Guodong
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study the infinite-horizon optimal control problem for N-network queueing systems, which consists of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: (1) minimizing the queueing (and idleness) cost, (2) minimizing the queueing cost while imposing a constraint on idleness at each server pool, and (3) minimizing the queueing cost while requiring fairness on idleness. The running costs can be any nonne...
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作者：Benchetrit, Yohann; Fiorini, Samuel; Huynh, Tony; Weltge, Stefan
作者单位：Universite Libre de Bruxelles
摘要：Let S subset of {0, 1}(n) and R be any polytope contained in [0, 1](n) with R boolean AND {0, 1}(n) = S. We prove that R has bounded Chvatal-Gomory rank (CG-rank) provided that S has bounded notch and bounded gap, where the notch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the facet coefficients of conv(S). Let H[(S) over bar] denote the subgraph of the n-cube induced by the vertices not...
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作者：Drusvyatskiy, Dmitriy; Lewis, Adrian S.
作者单位：University of Washington; University of Washington Seattle; Cornell University
摘要：The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may linearly bound the error-the distance to the solution set. We explain the observed linear convergence intuitively by proving the equivalence of such an error bound to a natural quadratic growth condition. Our approach generalizes to linear and quadratic convergence ...
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作者：Lacker, Daniel
作者单位：Columbia University
摘要：This paper studies curves of the form (rho(lambda X)(lambda >= 0), called risk profiles, where rho is a convex risk measure and X a random variable. Financially, this captures the sensitivity of risk to the size of the investment in X, which the original axiomatic foundations of convex risk measures suggest to interpret as liquidity risk. The shape of a risk profile is intimately linked with the tail behavior of X for some notable classes of risk measures, namely shortfall risk measures and op...
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作者：Berczi, Kristof; Frank, Andras
作者单位：Eotvos Lorand University
摘要：By generalizing a recent result of Hong, Liu and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple k-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmentin...
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作者：Cavazos-Cadena, Rolando
摘要：This work is concerned with Markov decision chains on a denumerable state space. The controller has a positive risk-sensitivity coefficient, and the performance of a control policy is measured by a risk-sensitive average cost criterion. Besides standard continuity-compactness conditions, it is assumed that the state process is communicating under any stationary policy, and that the simultaneous Doeblin condition holds. In this context, it is shown that if the cost function is bounded from belo...
