Mathematics of Operations Research

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second order subdifferential of ...

Logit dynamics is a form of randomized game dynamics in which players have a bias toward strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converge to the so-...

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and ergodic performance criteria. This class of games finds natural ...

We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In ...

Spectral functions on Euclidean Jordan algebras arise frequently in convex optimization models. Despite the success of primal-dual conic interior point solvers, there has been little work on enabling direct support for spectral cones, that is, proper ...

We present an accelerated or “look-ahead” version of the Newton–Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current iterate and the ...

We design novel mechanisms for welfare maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are ...

This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of graphon games based on a single typical player’s label-state distribution. In contrast, other recently proposed models of graphon games work ...

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The derivatives and their ...

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem and then solve the problem using the predicted values of the parameters. A natural loss function in this environment ...

In this paper, for partially observed Markov decision problems (POMDPs), we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and consequentially, we establish near ...

Convex optimization over the spectrahedron, that is, the set of all real n × n positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing, and statistics, mainly as a convex relaxation for ...

Let ρ be a general law-invariant convex risk measure, for instance, the average value at risk, and let X be a financial loss, that is, a real random variable. In practice, either the true distribution μ of X is unknown, or the numerical computation of ρ(μ) is ...

This paper introduces a discrete-time stochastic game class on Zd, which plays the role of a toy model for the well-known problem of stochastic homogenization of Hamilton–Jacobi equations. Conditions are provided under which the n-stage game value converges ...

We consider flows over time within the deterministic queueing model of Vickrey and study the solution concept of instantaneous dynamic equilibrium (IDE), in which flow particles select at every decision point a currently shortest path. The length of such ...

The stochastic multiarmed bandit (MAB) problem is a common model for sequential decision problems. In the standard setup, a decision maker has to choose at every instant between several competing arms; each of them provides a scalar random variable, ...

We consider mean-field contribution games, where players in a team choose some effort levels at each time period and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the ...

We study integer-valued matrices with bounded determinants. Such matrices appear in the theory of integer programs (IPs) with bounded determinants. For example, an IP can be solved in strongly polynomial time if the constraint matrix is bimodular: that is,...

We consider potential-based flow networks with terminal nodes at which flow can enter or leave the network and physical properties, such as voltages or pressures, are measured and controlled. We study conditions under which such a network can be reduced ...

There is an error in our paper [Paul A, Freund D, Ferber A, Shmoys DB, Williamson DP (2020) Budgeted prize-collecting traveling salesman and minimum spanning tree problems. Math. Oper. Res. 45(2):576–590]. In that paper, we consider constrained versions ...

Linear fixed-point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random observations to ...

This paper develops a novel adaptive, augmented, Lagrangian-based method to address the comprehensive class of nonsmooth, nonconvex models with a nonlinear, functional composite structure in the objective. The proposed method uses an adaptive mechanism ...

We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space H, aiming to shed light on the acceleration phenomenon for monotone inclusion problems, which unifies a broad class of optimization, saddle point, and ...