Mathematics of Operations Research

最新文章

• On the Control of Fork-Join Networks AI翻译
  作者：Ozkan, Erhun; Ward, Amy R.
  作者单位：University of Southern California
  摘要：Networks in which the processing of jobs occurs both sequentially and in parallel are prevalent in many application domains, such as computer systems, healthcare, manufacturing, and project management. The parallel processing of jobs gives rise to synchronization constraints that can be a main reason for job delay. In comparison with feed-forward queueing networks that have only sequential processing of jobs, the approximation and control of networks that have synchronization constraints is le...
• A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints AI翻译
  作者：Huchette, Joey; Vielma, Juan Pablo
  作者单位：Rice University; Massachusetts Institute of Technology (MIT)
  摘要：A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinea...
• Semidefinite Relaxations for Lebesgue and Gaussian Measures of Unions of Basic Semialgebraic Sets AI翻译
  作者：Lasserre, Jean B.; Emin, Youssouf
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：Given a finite Bard measure mu on R-n and basic semialgebraic sets Omega(i) subset of R-n, i=1, ..., p, we provide a systematic numerical scheme to approximate as closely as desired mu(U-i Omega(i)), when all moments of mu are available (and finite). More precisely, we provide a hierarchy of semidefinite programs whose associated sequence of optimal values is monotone and converges to the desired value from above. The same methodology applied to the complement R-n \ (U-i Omega(i))provides a mo...
• Product-Mix Auctions and Tropical Geometry AI翻译
  作者：Ngoc Mai Tran; Yu, Josephine
  作者单位：University of Texas System; University of Texas Austin; University of Bonn; University System of Georgia; Georgia Institute of Technology
  摘要：In a recent and ongoing work, Baldwin and Klemperer explore a connection between tropical geometry and economics. They give a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods. This result, which we call the unimodularity theorem, can also be traced back to the work of Danilov, Koshevoy, and Murota in discrete convex analysis. We give a new proof of the unimodularity theorem via the classical unimodularity theorem in integer programm...
• An Inverse Optimal Stopping Problem for Diffusion Processes AI翻译
  作者：Kruse, Thomas; Strack, Philipp
  作者单位：University of Duisburg Essen; University of California System; University of California Berkeley
  摘要：Let X be a one-dimensional diffusion and let g be a real-valued function depending on time and the value of X. This article analyzes the inverse optimal stopping problem of finding a time-dependent real-valued function pi depending only on time such that a given stopping time tau(star) is a solution of the stopping problem sup(tau) E[g(tau, X-tau) + pi(tau)]. Under regularity and monotonicity conditions, there exists such a transfer pi if and only if tau(star) is the first time when X exceeds ...
• Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models AI翻译
  作者：Cheung, Wang Chi; Simchi-Levi, David
  作者单位：Agency for Science Technology & Research (A*STAR); A*STAR - Institute of High Performance Computing (IHPC); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
  摘要：We study the classical multiperiod capacitated stochastic inventory control problems in a data-driven setting. Instead of assuming full knowledge of the demand distributions, we assume that the demand distributions can only be accessed through drawing random samples. Such data-driven models are ubiquitous in practice, where the cumulative distribution functions of the underlying random demand are either unavailable or too complex to work with. We consider the sample average approximation (SAA)...
• Polytope Conditioning and Linear Convergence of the Frank-Wolfe Algorithm AI翻译
  作者：Pena, Javier; Rodriguez, Daniel
  作者单位：Carnegie Mellon University; Carnegie Mellon University
  摘要：It is well known that the gradient descent algorithm converges linearly when applied to a strongly convex function with Lipschitz gradient. In this case, the algorithm's rate of convergence is determined by the condition number of the function. In a similar vein, it has been shown that a variant of the Frank-Wolfe algorithm with away steps converges linearly when applied to a strongly convex function with Lipschitz gradient over a polytope. In a nice extension of the unconstrained case, the al...
• Mixed-Integer Linear Representability, Disjunctions, and Chvatal Functions-Modeling Implications AI翻译
  作者：Basu, Amitabh; Martin, Kipp; Ryan, Christopher Thomas; Wang, Guanyi
  作者单位：Johns Hopkins University; University of Chicago; University System of Georgia; Georgia Institute of Technology
  摘要：Jeroslow and Lowe gave an exact geometric characterization of subsets of R-n that are projections of mixed-integer linear sets, also known as MILP-representable or MILP-R sets. We give an alternate algebraic characterization by showing that a set is MILP-R if and only if the set can be described as the intersection of finitely many affine Chvatal inequalities in continuous variables (termed AC sets). These inequalities are a modification of a concept introduced by Blair and Jeroslow. Unlike th...
• Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions AI翻译
  作者：Saldi, Naci; Basar, Tamer; Raginsky, Maxim
  作者单位：Ozyegin University; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players (agents) and the decentralized nature of this information. When the number of players is sufficiently large and the interactions among agents is of the mean-field type, one way to overcome this challenge is to investigate the infinite-population limit of the proble...
• Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Case AI翻译
  作者：Trybula, Jakub; Zawisza, Dariusz
  作者单位：Cracow University of Economics; Jagiellonian University
  摘要：We consider an incomplete market with a nontradable stochastic factor and a continuous-time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to find an optimal investment strategy and the value function. What is more, we show that our solution is also optimal for the classical Markowitz problem, and every optimal solution for the classical Marko...