Mathematics of Operations Research

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• A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies AI翻译
  作者：Fu, Guanxing; Horst, Ulrich; Xia, Xiaonyu
  作者单位：Hong Kong Polytechnic University; Hong Kong Polytechnic University; Humboldt University of Berlin; Humboldt University of Berlin; Wenzhou University
  摘要：We consider a mean-field control problem with ca`dla`g semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and we show that it is of linear-quadratic form and that its coefficients satisfy a coupled system of nonstandard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a s...
• A New Approach to Capacity Scaling Augmented with Unreliable Machine Learning Predictions AI翻译
  作者：Rutten, Daan; Mukherjee, Debankur
  作者单位：University System of Georgia; Georgia Institute of Technology
  摘要：Modern data centers suffer from immense power consumption. As a result, data center operators have heavily invested in capacity-scaling solutions, which dynamically deactivate servers if the demand is low and activate them again when the workload increases. We analyze a continuous-time model for capacity scaling, where the goal is to minimize the weighted sum of flow time, switching cost, and power consumption in an online fashion. We propose a novel algorithm, called adaptive balanced capacit...
• Constrained Information Design AI翻译
  作者：Doval, Laura; Skreta, Vasiliki
  作者单位：Columbia University; Centre for Economic Policy Research - UK; University of Texas System; University of Texas Austin; University of London; University College London
  摘要：We provide tools to analyze information design problems subject to constraints. We do so by extending an insight by Le Treust and Tomala to the case of multiple inequality and equality constraints. Namely, that an information design problem subject to constraints can be represented as an unconstrained information design problem with additional states, one for each constraint. Thus, without loss of generality, optimal solutions induce as many posteriors as the number of states and constraints. ...
• Relaxed Equilibria for Time-Inconsistent Markov Decision Processes AI翻译
  作者：Bayraktar, Erhan; Huang, Yu-Jui; Wang, Zhenhua; Zhou, Zhou
  作者单位：University of Michigan System; University of Michigan; University of Colorado System; University of Colorado Boulder; Shandong University; Shandong University; University of Sydney
  摘要：This paper considers an infinite-horizon Markov decision process (MDP) that allows for general nonexponential discount functions in both discrete and continuous time. Because of the inherent time inconsistency, we look for a randomized equilibrium policy (i.e., relaxed equilibrium) in an intrapersonal game between an agent's current and future selves. When we modify the MDP by entropy regularization, a relaxed equilibrium is shown to exist by a nontrivial entropy estimate. As the degree of reg...
• Exit Game with Private Information AI翻译
  作者：Kwon, H. Dharma; Palczewski, Jan
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Leeds
  摘要：The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about their competitor's exit value. We construct an equilibrium for a large class of payoff flows driven by a general one-dimensional diffusion. In the equilibrium, the players employ sophisticated exit strategies involving both the state variable and the posterio...
• A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length AI翻译
  作者：Vazirani, Vijay V.
  作者单位：University of California System; University of California Irvine
  摘要：The Micali-Vazirani (MV) algorithm for finding a maximum cardinality matching in general graphs, which was published in 1980, remains to this day the most efficient known algorithm for the problem. The current paper gives the first complete and correct proof of this algorithm. The MV algorithm resorts to finding minimum-length augmenting paths. However, such paths fail to satisfy an elementary property, called breadth first search honesty in this paper. In the absence of this property, an expo...
• Probabilistic Bounds on the k-Traveling Salesman Problem and the Traveling Repairman Problem AI翻译
  作者：Blanchard, Moise; Jacquillat, Alexandre; Jaillet, Patrick
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact permissions@informs.org. The Publisher does not warrant or guarantee the article's accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, produ...
• Unbiased Time-Average Estimators for Markov Chains AI翻译
  作者：Kahale, Nabil
  作者单位：heSam Universite; ESCP Business School
  摘要：We consider a time-average estimator fk of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of f(k) has a limit mu as the number of time steps goes to infinity. We describe a modification of f(k) that yields an unbiased estimator f(k) of mu. It is shown that f(k) is square integrable and has finite expected running time. Under certain conditions, f(k) can be built without any precomputations and is asymptotically at least as efficient as f(k), up to a m...
• Dynamic Pricing Provides Robust Equilibria in Stochastic Ridesharing Networks AI翻译
  作者：Cashore, J. Massey; Frazier, Peter I.; Tardos, Eva
  作者单位：Cornell University; Cornell University
  摘要：Using prices induced by dual variables of a centralized optimization problem induces welfare-optimal equilibria among strategic drivers. We reveal a stark deficiency of such static pricing algorithms: it is possible for them to induce additional equilibria with arbitrarily low social welfare. Moreover, small perturbations to the marketplace, such as those caused by idiosyncratic randomness or model misspecification, can cause the welfare-optimal equilibrium to be Pareto-dominated (in terms of ...
• A Riemannian Smoothing Steepest Descent Method for Non-Lipschitz Optimization on Embedded Submanifolds of Rn AI翻译
  作者：Zhang, Chao; Chen, Xiaojun; Ma, Shiqian
  作者单位：Beijing Jiaotong University; Hong Kong Polytechnic University; Rice University
  摘要：In this paper, we study the generalized subdifferentials and the Riemannian gradient subconsistency that are the basis for non-Lipschitz optimization on embedded sub manifolds of R-n. We then propose a Riemannian smoothing steepest descent method for non-Lipschitz optimization on complete embedded submanifolds of Rn. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary point associated with the smoothing function emp...