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作者：Perchet, Vianney; Quincampoix, Marc
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We represent any repeated game with partial monitoring as an abstract repeated game with full monitoring where outcomes are probability measures, to be interpreted as the maximal information the players can obtain in the original game. One of our objectives is to define and generalize Blackwell's approachability theory in this space of probability measures. We characterize approachable sets with, as usual, a simple and complete formulation for convex sets. Translated back into the original gam...
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作者：Basu, Amitabh; Martin, Kipp; Ryan, Christopher Thomas
作者单位：Johns Hopkins University; University of Chicago
摘要：Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. We extend Fourier-Motzkin elimination to semi-infinite linear programs, which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability. Extending the Fourier-Motzkin elimination procedure to s...
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作者：Gensbittel, Fabien
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole
摘要：This work is devoted to extend several asymptotic results concerning repeated games with incomplete information on one side. The model we consider is a generalization of the classical model of Aumann and Maschler (Aumann et al. [Aumann RJ, Maschler M, Stearns RE (1995) Repeated Games with Incomplete Information (MIT Press, Cambridge, MA)]) to infinite action spaces and partial information. We prove an extension of the classical Cav(u) Theorem in this model for both the lower and upper value fu...
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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：Boxma, Onno; Perry, David; Zacks, Shelley
作者单位：Eindhoven University of Technology; Eindhoven University of Technology; University of Haifa; State University of New York (SUNY) System; Binghamton University, SUNY
摘要：We consider a stochastic fluid EOQ-type model with demand rates operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases linearly at rate, beta(H) during the periods of high demand, and at rate, beta(L) < beta(H) at periods of low demand. Refilling of the inventory level to level q is required when the first of two e...
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作者：Conforti, Michele; Cornuejols, Gerard; Daniilidis, Aris; Lemarechal, Claude; Malick, Jerome
作者单位：University of Padua; Carnegie Mellon University; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (CGF) and we develop a formal theory for them, largely based on convex analysis. They are...
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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：Bhaskar, Umang; Fleischer, Lisa; Hoy, Darrell; Huang, Chien-Chung
作者单位：California Institute of Technology; Dartmouth College; Northwestern University; Chalmers University of Technology
摘要：In routing games with infinitesimal players, it follows from well-known convexity arguments that equilibria exist and are unique. In routing games with atomic players with splittable flow, equilibria exist, but uniqueness of equilibria has been demonstrated only in limited cases: in two-terminal nearly parallel graphs, when all players control the same amount of flow, and when latency functions are polynomials of degree at most three. There are no known examples of multiple equilibria in these...
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作者：Huynh Van Ngai; Phan Nhat Tinh
作者单位：Hue University
摘要：Metric subregularity and regularity of multifunctions are fundamental notions in variational analysis and optimization. Using the concept of strong slope, in this paper we first establish a criterion for metric subregularity of multifunctions between metric spaces. Next, we use a combination of abstract coderivatives and contingent derivatives to derive verifiable first order conditions ensuring metric subregularity of multifunctions between Banach spaces. Then using second order approximation...
