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作者：Jhunjhunwala, Prakirt R.; Zubeldia, Martin; Maguluri, Siva Theja
作者单位：Columbia University; University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology
摘要：We consider a load-balancing system composed of a fixed number of singleserver queues operating under the well-known join-the-shortest queue policy and where jobs/customers are impatient and abandon if they do not receive service after some (random) amount of time. In this setting, we characterize the centered and appropriately scaled steady-state queue-length distribution (hereafter referred to as limiting distribution) in the limit as the abandonment rate goes to zero at the same time as the...
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作者：Kang, Weining
作者单位：University System of Maryland; University of Maryland Baltimore County
摘要：In this paper, under mild conditions on the arrival, service, and patience time distributions, we establish the well-posedness of the fluid model of a multiclass manyserver queueing model with differentiated service and patience times operated under the global FCFS service discipline. In particular, the well-posedness of the fluid model is established through the study of the existence and uniqueness of fixed points of a certain functional map of Volterra type. In addition, by showing a local ...
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作者：Han, Shaoning; Gomez, Andres
作者单位：National University of Singapore; University of Southern California
摘要：We study the mixed-integer epigraph of a special class of convex functions with nonconvex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions. Extended formulations describing the convex hull of such sets can easily be constructed via disjunctive programming although a direct application of this method often yields pr...
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作者：Gupte, Akshay; Zhu, Yiran
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh
摘要：Computing the maximum size of an independent set in a graph is a famously hard combinatorial problem that has been well studied for various classes of graphs. When it comes to random graphs, the classic Erdos-Renyi-Gilbert random graph G(n,p) has been analyzed and shown to have the largest independent sets of size Theta(logn) with high probability (w.h.p.) This classic model does not capture any dependency structure between edges that can appear in real-world networks. We define random graphs ...
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作者：Ahmadi, Amir Ali; Guenluek, Oktay
作者单位：Princeton University; Cornell University
摘要：A robust-to-dynamics optimization (RDO) problem is an optimization problem spe- cified by two pieces of input: (i) a mathematical program (an objective function f: R -> R and a feasible set QCR) and (it) a dynamical system (a map g: R->). Its goal is to minimize f over the set SCQ of initial conditions that forever remain in Q under g. The focus of this paper is on the case where the mathematical program is a linear program and where the dynamical system is either a known linear map or an unce...
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作者：Luner, Alan; Grimmer, Benjamin
作者单位：Johns Hopkins University
摘要：This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a convex combination of the iterates (averaging) or a generic combination of the iterates (extrapolation). For several common stepsize sequences, including recently developed accelerated periodically long stepsize schemes, we show averaging cannot improve gradien...
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作者：Han, Xia; Wang, Qiuqi; Wang, Ruodu; Xia, Jianming
作者单位：Nankai University; Nankai University; University System of Georgia; Georgia State University; University of Waterloo; Chinese Academy of Sciences
摘要：In the literature on risk measures, cash subadditivity was proposed to replace cash additivity, motivated by the presence of stochastic or ambiguous interest rates and defaultable contingent claims. Cash subadditivity has been traditionally studied together with quasi-convexity, in a way similar to cash additivity with convexity. In this paper, we study cash-subadditive risk measures without quasi-convexity. One of our major results is that a general cash-subadditive risk measure can be repres...
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作者：Xia, Li; Ma, Shuai
作者单位：Sun Yat Sen University
摘要：Dynamic optimization of mean and variance in Markov decision processes (MDPs) is a long-standing challenge caused by the failure of dynamic programming. In this paper, we propose a new approach to finding the globally optimal policy for combined metrics of steady-state mean and variance in an infinite-horizon undiscounted MDP. By introducing the concepts of pseudo mean and pseudo variance, we convert the original problem to a bilevel MDP problem, where the inner one is a standard MDP optimizin...
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作者：Ramachandran, Akshay; Shu, Kevin; Wang, Alex L.
作者单位：University System of Georgia; Georgia Institute of Technology; Purdue University System; Purdue University
摘要：This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices SO(n). Such problems are non-convex because of the constraint X E SO(n). Nonetheless, we show that certain linear images of SO(n) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of SO(n) is convex and that the projection of SO(...
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作者：Guan, Guohui; Liang, Zongxia; Xia, Jianming
作者单位：Renmin University of China; Renmin University of China; Tsinghua University; Chinese Academy of Sciences
摘要：This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous -time market. The investor is uncertain about the risky asset's drift term and updates the subjective belief according to the Bayesian rule. A verification theorem is established, and an equilibrium strategy can be decomposed into a myopic demand and two hedging demands. When the prior is Gaussian, we provide an equilibrium solution in closed form. Moreover, a puzzle in the numerical re...
