Mathematics of Operations Research

最新文章

• Approximation Algorithms for Dynamic Assortment Optimization Models AI翻译
  作者：Aouad, Ali; Levi, Retsef; Segev, Danny
  作者单位：University of London; London Business School; Massachusetts Institute of Technology (MIT); University of Haifa
  摘要：We consider the single-period joint assortment and inventory planning problem with stochastic demand and dynamic substitution across products, motivated by applications in highly differentiated markets, such as online retailing and airlines. This class of problems is known to be notoriously hard to deal with from a computational standpoint. In fact, prior to the present paper, only a handful of modeling approaches were shown to admit provably good algorithms, at the cost of strong restrictions...
• Generating Functions of Weighted Voting Games, MacMahon's Partition Analysis, and Clifford Algebras AI翻译
  作者：Neto, Antonio Francisco
  作者单位：Universidade Federal de Ouro Preto
  摘要：MacMahon's Partition Analysis (MPA) is a combinatorial tool used in partition analysis to describe the solutions of a linear diophantine system. We show that MPA is useful in the context of weighted voting games. We introduce a new generalized generating function that gives, as special cases, extensions of the generating functions of the Banzhaf, Shapley-Shubik, Banzhaf-Owen, symmetric coalitional Banzhaf, and Owen power indices. Our extensions involve any coalition formation related to a line...
• Weak Stability of l1-Minimization Methods in Sparse Data Reconstruction AI翻译
  作者：Zhao, Yun-Bin; Jiang, Houyuan; Luo, Zhi-Quan
  作者单位：University of Birmingham; University of Cambridge; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen
  摘要：As one of the most plausible convex optimization methods for sparse data reconstruction, l(1)-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as the restricted isometry property, null space property, and mutual coherence. In this paper, we propose a unified means to develop the so-called weak stability theory for l(1)-minimization methods under the condition ...
• Discrete Approximation and Quantification in Distributionally Robust Optimization AI翻译
  作者：Liu, Yongchao; Pichler, Alois; Xu, Huifu
  作者单位：Dalian University of Technology; Technische Universitat Chemnitz; University of Southampton
  摘要：Discrete approximation of probability distributions is an important topic in stochastic programming. In this paper, we extend the research on this topic to distributionally robust optimization (DRO), where discretization is driven by either limited availability of empirical data (samples) or a computational need for improving numerical tractability. We start with a one-stage DRO where the ambiguity set is defined by generalized prior moment conditions and quantify the discrepancy between the d...
• On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming AI翻译
  作者：Liu, Ya-Feng; Liu, Xin; Ma, Shiqian
  作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of California System; University of California Davis
  摘要：In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian subproblem in the proposed IAL framework is weaker and potentially much easier to check than the one used in most of the existing IAL frameworks/methods. We analyze the global co...
• Location Games on Networks: Existence and Efficiency of Equilibria AI翻译
  作者：Fournier, Gaetan; Scarsini, Marco
  作者单位：Aix-Marseille Universite; Luiss Guido Carli University
  摘要：We consider a game where a finite number of retailers choose a location, given that their potential consumers are distributed on a network. Retailers do not compete on price but only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost borne by the consumers with the cost that could be achieved if the retailers followed the dic...
• Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models AI翻译
  作者：Shiraya, Kenichiro; Takahashi, Akihiko
  作者单位：University of Tokyo
  摘要：This paper presents a new approximation formula for pricing multidimensional discretely monitored average options in a local-stochastic volatility (LSV) model with jump by applying an asymptotic expansion technique. Moreover, it provides a justification of the approximation method with some asymptotic error estimates for general payoff functions. Particularly, our model includes local volatility functions and jump components in the underlying asset price as well as its volatility processes. To...
• Efficient Simulation of High Dimensional Gaussian Vectors AI翻译
  作者：Kahale, Nabil
  作者单位：heSam Universite; ESCP Business School
  摘要：We describe a Markov chain Monte Carlo method to approximately simulate a centered d-dimensional Gaussian vector X with given covariance matrix. The standard Monte Carlo method is based on the Cholesky decomposition, which takes cubic time and has quadratic storage cost in d. By contrast, the additional storage cost of our algorithm is linear in d. We give a bound on the quadratic Wasserstein distance between the distribution of our sample and the target distribution. Our method can be used to...
• Completely Positive Binary Tensors AI翻译
  作者：Fan, Jinyan; Nie, Jiawang; Zhou, Anwa
  作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; University of California System; University of California San Diego; Shanghai University
  摘要：A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative vectors. This paper characterizes completely positive binary tensors. We show that a binary tensor is completely positive if and only if it satisfies two linear matrix inequalities. This result can be used to determine whether a binary tensor is completely positive or not. When it is, we give an algorithm for computing its cp-rank and the decomposition. When the order is odd, we show that the cp-rank ...
• Perfect Sampling of Generalized Jackson Networks AI翻译
  作者：Blanchet, Jose; Chen, Xinyun
  作者单位：Stanford University; Wuhan University
  摘要：We provide the first perfect sampling algorithm for a generalized Jackson network of first-in, first-out queues under arbitrary topology and non-Markovian assumptions on the input of the network. We assume (in addition to stability) that the interarrival and service times of customers have a finite moment-generating function in a neighborhood of the origin, and the interarrival times have unbounded support.