Mathematics of Operations Research

最新文章

• Correlated Equilibria in Large Anonymous Bayesian Games AI翻译
  作者：Koessler, Frederic; Scarsini, Marco; Tomala, Tristan
  作者单位：Luiss Guido Carli University
  摘要：We consider multipopulation Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player's own action, the distribution of players' actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibr...
• Fair Congested Assignment AI翻译
  作者：Bogomolnaia, Anna; Moulin, Herve
  作者单位：University of Glasgow; Centre National de la Recherche Scientifique (CNRS)
  摘要：We must assign n agents to m posts subject to negative congestion; what assignment is fair and efficient? If congestion is anonymous (each agent adds one unit), it is always possible to assign each agent to one of the agent's top n out of the n x m feasible allocations. This ordinal interpretation of ex ante fairness can be adjusted if congestion is weighted (agent-specific). An assignment is competitive if I don't want to move to an empty post or to an occupied one at its current congestion l...
• Inexact Bregman Proximal Gradient Method and Its Inertial Variant with Absolute and Partial Relative Stopping Criteria AI翻译
  作者：Yang, Lei; Toh, Kim-Chuan
  作者单位：Sun Yat Sen University; National University of Singapore
  摘要：The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been redeveloped for minimizing convex composite problems without the global Lipschitz gradient continuity assumption. This makes the BPGM appealing for a wide range of applications, and hence, it has received growing attention in recent years. However, most existing convergence results are obtained only under the assumption that the involved subproblems are...
• Convergence of Augmented Lagrangian Methods for Composite Optimization Problems AI翻译
  作者：Hang, Nguyen Thi Van; Sarabi, Ebrahim
  作者单位：Nanyang Technological University; Vietnam Academy of Science & Technology (VAST); University System of Ohio; Miami University
  摘要：Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property called the semistability of second subderivatives and demonstrate that it is widely satisfied for numerous classes of functions, which is important for applications in constrained and composite optimization problems. Using the latte...
• On Interim Envy-Free Allocation Lotteries AI翻译
  作者：Caragiannis, Ioannis; Kanellopoulos, Panagiotis; Kyropoulou, Maria
  作者单位：Aarhus University; University of Essex
  摘要：With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too-stringent notion of ex post envy-freeness and the very weak notion of ex ante envy freeness. Our analysis relates iEF to other fairness notions as well and reveals trade-offs between iEF and efficiency. Even though several of ...
• Rockafellian Relaxation and Stochastic Optimization Under Perturbations AI翻译
  作者：Royset, Johannes O.; Chen, Louis L.; Eckstrand, Eric
  作者单位：University of Southern California; United States Department of Defense; United States Navy; Naval Postgraduate School
  摘要：In practice, optimization models are often prone to unavoidable inaccuracies because of dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on conservative decisions. We develop, in contrast, an optimistic framework based on Rockafellian relaxations in which optimization is conducted not only over the original decision space but also jointly with a choice of model perturbation. The framework enables us to ad...
• How to Design a Stable Serial Knockout Competition AI翻译
  作者：Lambers, Roel; Pendavingh, Rudi; Spieksma, Frits
  作者单位：Eindhoven University of Technology
  摘要：We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a serial knockout competition (SKC). This format has recently been adopted by the Professional Darts Corporation. Depending on the seedings of the players used for each of the knockout tournaments, players can meet in the various rounds (e.g., first round, second round ... semifinal, final) of the knockout tournaments. Following a fairness principle of treating all playe...
• Is There a Golden Parachute in Sannikov's Principal-Agent Problem? AI翻译
  作者：Possamai, Dylan; Touzi, Nizar
  作者单位：New York University; New York University Tandon School of Engineering
  摘要：This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov in the extended context allowing for possibly different discount rates for both parties. The agent's problem is to seek for optimal effort given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirem...
• Stationary Points of a Shallow Neural Network with Quadratic Activations and the Global Optimality of the Gradient Descent Algorithm AI翻译
  作者：Gamarnik, David; Kizildag, Eren C.; Zadik, Ilias
  作者单位：Massachusetts Institute of Technology (MIT); Columbia University; Yale University
  摘要：We consider the problem of training a shallow neural network with quadratic activation functions and the generalization power of such trained networks. Assuming that the samples are generated by a full rank matrix W* of the hidden network node weights, we obtain the following results. We establish that all full -rank approximately stationary solutions of the risk minimization problem are also approximate global optimums of the risk (in -sample and population). As a consequence, we establish th...
• Positivstellensatze and Moment Problems with Universal Quantifiers AI翻译
  作者：Hu, Xiaomeng; Klep, Igor; Nie, Tiawang
  作者单位：University of California System; University of California San Diego; University of Ljubljana; University of Primorska
  摘要：This paper studies Positivstellensatze and moment problems for sets K that are given by universal quantifiers. Let Q be the closed set of universal quantifiers. Fix a finite nonnegative Borel measure whose support is Q and assume it satisfies the multivariate Carleman condition. First, we prove a Positivstellensatz with universal quantifiers: if a polynomialf is positive on K, then f belongs to the associated quadratic module, under the archimedeanness assumption. Second, we prove some necessa...