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作者：Li, Min; Yuan, Xiaoming
作者单位：Southeast University - China; Hong Kong Baptist University
摘要：Recently, a strictly contractive Peaceman-Rachford splitting method (PRSM) was proposed for a separable convex minimization model whose variables are subject to some linear constraints and two additional generic constraints. In general, the strictly contractive PRSM requires to solve two constrained minimization subproblems at each iteration. In this paper, we consider the case where the additional constraints on variables are positive orthants and apply the well-developed logarithmic-quadrati...
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作者：Yu, Huizhen; Bertsekas, Dimitri P.
作者单位：University of Alberta; Massachusetts Institute of Technology (MIT)
摘要：We consider stochastic optimal control models with Borel spaces and universally measurable policies. For such models the standard policy iteration is known to have difficult measurability issues and cannot be carried out in general. We present a mixed value and policy iteration method that circumvents this difficulty. The method allows the use of stationary policies in computing the optimal cost function in a manner that resembles policy iteration. It can also be used to address similar diffic...
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作者：Amarante, Massimiliano
作者单位：Universite de Montreal; Universite de Montreal
摘要：In the context of decision making under uncertainty, I formalize the concept of analogy: an analogy between two decision problems is a mapping that transforms one problem into the other while preserving the problem's structure. After identifying the basic structure of a decision problem, I introduce the concepts of analogical reasoning operator and of analogical reasoning preference. The former maps the decision problem at hand into a family of decision problems, which are analogous to the pro...
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作者：Gensbittel, Fabien; Renault, Jerome
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：We consider zero-sum repeated games with incomplete information on both sides, where the states privately observed by each player follow independent Markov chains. It generalizes the model, introduced by Aumann and Maschler in the sixties and solved by Mertens and Zamir in the seventies, where the private states of the players were fixed. It also includes the model introduced in Renault [19] [Renault J (2006) The value of Markov chain games with lack of information on one side. Math. Oper. Res...
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作者：Zhang, Xiaowei; Blanchet, Jose; Giesecke, Kay; Glynn, Peter W.
作者单位：Hong Kong University of Science & Technology; Columbia University; Stanford University
摘要：We establish a central limit theorem and a large deviations principle for affine point processes, which are stochastic models of correlated event timing widely used in finance and economics. These limit results generate closed-form approximations to the distribution of an affine point process. They also facilitate the construction of an asymptotically optimal importance sampling estimator of tail probabilities. Numerical tests illustrate our results.
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作者：Dieker, A. B.; Vempala, Santosh S.
作者单位：Columbia University; University System of Georgia; Georgia Institute of Technology
摘要：Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets.
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作者：Kwon, H. Dharma; Zhang, Hongzhong
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Columbia University
摘要：We investigate a game of singular control and strategic exit in a model of competitive market share control. In the model, each player can make irreversible investments to increase his market share, which is modeled as a diffusion process. In addition, each player has an option to exit the market at any point in time. We formulate a verification theorem for best responses of the game and characterize Markov perfect equilibria (MPE) under a set of verifiable assumptions. We find a class of MPEs...
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作者：Kalai, Gil; Mossel, Elchanan
作者单位：Hebrew University of Jerusalem; Yale University; University of Pennsylvania; University of California System; University of California Berkeley
摘要：A key fact in the theory of Boolean functions f : {0, 1}(n) -> {0, 1} is that they often undergo sharp thresholds. For example, if the function f : {0, 1}(n) -> {0, 1} is monotone and symmetric under a transitive action with E-p[f] = epsilon and E-q[f] = 1 - epsilon, then q - p -> 0 as n -> infinity. Here E-p denotes the product probability measure on {0, 1}(n) where each coordinate takes the value 1 independently with probability p. The fact that symmetric functions undergo sharp thresholds i...
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作者：Bensoussan, Alain; Cadenillas, Abel; Koo, Hyeng Keun
作者单位：University of Texas System; University of Texas Dallas; City University of Hong Kong; University of Alberta; Ajou University
摘要：We propose and solve a general entrepreneurial/managerial decision-making problem. Instead of employing concave objective functions, we use a broad class of nonconcave objective functions. We approach the problem by a martingale method. We show that the optimization problem with a nonconcave objective function has the same solution as the optimization problem when the objective function is replaced by its concave hull, and thus the problems are equivalent to each other. The value function is s...
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作者：Huynh Van Ngai; Thera, Michel
作者单位：Universite de Limoges; Federation University Australia
摘要：In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings. We then apply these characterizations to establish a coderivative type criterion for directional metric regularity as well as for the robustness of metric re...
