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作者：Cavazos-Cadena, R; Montes-de-Oca, R
作者单位：Universidad Autonoma Metropolitana - Mexico
摘要：This work concerns discrete-time Markov decision chains with finite state space and bounded costs. The controller has constant risk sensitivity A, and the performance of a control policy is measured by the corresponding risk-sensitive average cost criterion. Assuming that the optimality equation has a solution, it is shown that the value iteration scheme can be implemented to obtain, in a finite number of steps, (1) an approximation to the optimal A-sensitive average cost with an error less th...
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作者：Cheung, D; Cucker, F; Peña, J
作者单位：Carnegie Mellon University
摘要：In recent years, several condition numbers were defined for a variety of linear programming problems based upon relative distances to ill-posedness. In this paper, we provide a unifying view of soma: of these condition numbers. To do so, we introduce yet another linear programming problem and show that its distance to ill-posedness naturally captures the most commonly used distances to ill-posedness.
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作者：Nickel, S; Puerto, J; Rodriguez-Chia, AM
作者单位：Saarland University; University of Sevilla; Universidad de Cadiz
摘要：In this paper, we deal with single facility location problems in a general normed space in which the existing facilities are represented by convex sets of points. The criterion to be satisfied by the service facility is the minimization of an increasing, convex function of the distances from the service facility to the closest point of each demand set. We obtain a geometrical characterization of the set of optimal solutions for this problem. Two remarkable cases-the classical Weber problem and...
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作者：Atar, R; Dupuis, P; Shwartz, A
作者单位：Technion Israel Institute of Technology; Brown University
摘要：We consider the problem of risk-sensitive control of a stochastic network. In controlling such a network, an escape-time criterion can be useful if one wishes to regulate the occurrence of large buffers and buffer overflow. In this paper a risk-sensitive escape time criterion is formulated, which in comparison to the ordinary escape-time criteria penalizes exits that occur on short time intervals more heavily. The properties of the risk-sensitive problem are studied in the large buffer limit a...
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作者：Shapiro, A
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We discuss in this paper a class of nonsmooth functions which can be represented, in a neighborhood of a considered point, as a composition of a positively homogeneous convex function and a smooth mapping which maps the considered point into the null vector. We argue that this is a sufficiently rich class of functions and that such functions have various properties useful for purposes of optimization.
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作者：Yildirim, EA
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We study the asymptotic behavior of the interior-point bounds arising from the work of Yildirim and Todd on sensitivity analysis in semidefinite programming in comparison with the optimal partition bounds. We introduce a weaker notion of nondegeneracy and discuss its implications. For perturbations of the right-hand-side vector or the cost matrix, we show that the interior-point bounds evaluated on the central path using the Monteiro-Zhang family of search directions converge (as the duality g...
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作者：Lasserre, JB; Zeron, ES
作者单位：Centre National de la Recherche Scientifique (CNRS); Instituto Politecnico Nacional - Mexico
摘要：Given a convex rational polytope Omega(b) := {x is an element of R-+(n)\ Ax=b}, we consider the function b-->f (b), which counts the nonnegative integral points of Omega(b). A closed form expression of its Z-transform z-->F(z) is easily obtained so that f (b) can be computed as the inverse Z-transform of F. We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a convex integer polytope Omega. We also provide an alterna...
