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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：Fujishige, S; Yang, ZF
作者单位：Kyoto University; Yale University
摘要：In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the existence of core (and equilibrium) in a two-sided matching model. Since then, this condition has often been used in the literature on matching models and equilibrium models in the presence of indivisibilities. In this paper we prove that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is an M-#-concave function defined on the unit-hypercube, which is 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：Datta, RS
作者单位：University of California System; University of California Berkeley
摘要：Every real algebraic variety is isomorphic to the set. of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an N-person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreover, there exist isolated Nash equilibria of arbitrary topological degree.
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作者：Clark, SA
作者单位：University of Kentucky
摘要：This paper constructs an infinite-dimensional version of the Duality Theorem for a Linear Program (LP). The algebraic dual LP is replaced with a new program called the topological dual LP that closes the range of the adjoint operator. Under some mild nondegeneracy conditions involving strict positivity, the new Duality Theorem asserts that the optimal value of the primal LP equals the optimal value of the topological dual LP. Some applications to mathematical finance are also included.
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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：Zalinescu, C
作者单位：Martin Luther University Halle Wittenberg
摘要：In a recent paper Li and Singer (1998) introduced the notion of global error bound for a convex multifunction at a point of its domain. They showed the existence of such a global error bound when the-image of the multifunction at the respective point is bounded and conjectured a result for the case when the image is not bounded. In this paper we solve their conjecture with a positive answer. For this we establish a criterion for the existence of a global error bound using the Pompeiu-Hausdorff...
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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...
