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作者：Ahmadi, Amir Ali; El Khadir, Bachir
作者单位：Princeton University
摘要：We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data vary polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value of the TV-SDP. Moreover, by using a Positivstellensatz (positive locus theorem) on univariate polynomial matrices, we show that the best ...
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作者：Ye, Heng-Qing; Yao, David D.
作者单位：Hong Kong Polytechnic University; Columbia University
摘要：In a prior study [Ye HQ, Yao DD (2016) Diffusion limit of fair resource control- Stationary and interchange of limits. Math. Oper. Res. 41(4):1161-1207.] focusing on a class of stochastic processing network with fair resource control, we justified the diffusion approximation (in the context of the interchange of limits) provided that the pth moment of the workloads are bounded. To this end, we introduced the so-called bounded workload condition, which requires the workload process be bounded b...
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作者：Dogan, Battal; Dogan, Serhat; Yildiz, Kemal
作者单位：University of Bristol; Ihsan Dogramaci Bilkent University
摘要：Each capacity filling and substitutable choice rule is known to have a maximizer-collecting representation: There exists a list of priority orderings such that from each choice set that includes more alternatives than the capacity, the choice is the union of the priority orderings' maximizers. We introduce the notion of a critical set and constructively prove that the number of critical sets for a choice rule determines its smallest-size maximizer-collecting representation. We show that respon...
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作者：Pivato, Marcus
作者单位：CY Cergy Paris Universite
摘要：We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g., consumption bundles) is a topological space, and intertemporal plans (e.g., consumption streams) must be continuous functions of time. We assume that the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility func...
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作者：Keppo, Jussi; Reppen, A. Max; Soner, H. Mete
作者单位：National University of Singapore; National University of Singapore; Boston University; Princeton University
摘要：We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are given by discrete time processes. Moreover, between two dividend payments, the structure allows for other types of control; we consider the possibility of equity issuance at any point in time. The value is characterized as the fixed point of an optimal contro...
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作者：Feldman, Vitaly; Guzman, Cristobal; Vempala, Santosh
作者单位：Apple Inc; Pontificia Universidad Catolica de Chile; Pontificia Universidad Catolica de Chile; University System of Georgia; Georgia Institute of Technology
摘要：Stochastic convex optimization, by which the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research, and other areas. We study the complexity of stochastic convex optimization given only statistical query (SQ) access to the objective function. We show that well-known and popular first-order iterative methods can be implemented using only statistical queries. For many cases ...
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作者：Dadush, Dan; Vegh, Laszlo A.; Zambelli, Giacomo
作者单位：University of London; London School Economics & Political Science
摘要：We present a new class of polynomial-time algorithms for submodular function minimization (SFM) as well as a unified framework to obtain strongly polynomial SFM algorithms. Our algorithms are based on simple iterative methods for the minimum-norm problem, such as the conditional gradient and Fujishige-Wolfe algorithms. We exhibit two techniques to turn simple iterative methods into polynomial-time algorithms. First, we adapt the geometric rescaling technique, which has recently gained attentio...
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作者：Gupta, Varun; Moseley, Benjamin; Uetz, Marc; Xie, Qiaomin
作者单位：University of Chicago; Carnegie Mellon University; University of Twente; Cornell University
摘要：This corrigendum fixes an incorrect claim in the paper Gupta et al. [Gupta V, Moseley B, Uetz M, Xie Q (2020) Greed works-online algorithms for unrelated machine stochastic scheduling. Math. Oper. Res. 45(2):497-516.], which led us to claim a performance guarantee of 6 for a greedy algorithm for deterministic online scheduling with release times on unrelated machines. The result is based on an upper bound on the increase of the objective function value when adding an additional job j to a mach...
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作者：Liu, Fangda; Wang, Ruodu
作者单位：University of Waterloo
摘要：The notion of tail risk has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in bank...
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作者：Ma, Jin; Wong, Ting-Kam Leonard; Zhang, Jianfeng
作者单位：University of Southern California; University of Toronto
摘要：We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not subadditive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time inconsistency, that is, the usual tower property fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce...
