Mathematics of Operations Research

We study the efficiency of oligopoly equilibria (OE) in congested markets. The motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network. We show that increasing competition among ...

Variational inequality representations are set up for a general Walrasian model of consumption and production with trading in a market. The variational inequalities are of functional rather than geometric type and therefore are able to accommodate a ...

We consider a nonhomogeneous infinite-horizon Markov Decision Process (MDP) problem with multiple optimal first-period policies. We seek an algorithm that, given finite data, delivers an optimal first-period policy. Such an algorithm can thus ...

This paper deals with continuous-time Markov decision processes in Polish spaces, under an expected discounted reward criterion. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates ...

Over the years, various lift-and-project methods have been proposed to construct hierarchies of successive linear or semidefinite relaxations of a 0--1 polytope P ⊆ Rⁿ that converge to P in n steps. Many such methods have been shown to require n steps ...

In this paper, by assuming that a non-Lipschitz penalty function is exact, new conditions for the existence of Lagrange multipliers are established for an inequality and equality-constrained continuously differentiable optimization problem. This is done ...

A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions U_n, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, ...

We consider empirical approximations (sample average approximations) of two-stage stochastic mixed-integer linear programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory ...

The marriage model due to Gale and Shapley [Gale, D., L. S. Shapley. 1962. College admissions and the stability of marriage. Amer. Math. Monthly69 9--15] and the assignment model due to Shapley and Shubik [Shapley, L. S., M. Shubik. 1972. The assignment ...

In this paper we consider infinite horizon discrete-time optimal control of Markov decision processes (MDPs) with finite state spaces and compact action sets. We restrict attention to unicost MDPs, which form a class that contains all the weakly ...

Using the variational analysis technique, in terms of the epi-coderivative, we provide Lagrange multiplier rules for a class of semi-infinite optimization problems where all functions are lower semicontinuous or locally Lipschitz.

In this work, we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process. We use backward stochastic differential equations (BSDEs) and Snell envelopes. Finally, we give some numerical ...

This paper presents an extension of the Poincaré-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M, defined by a finite number of smooth inequality constraints. Given a function F: M → Rⁿ, we define ...

We consider the problem of selfish routing in a congested network shared by several users, where each user wishes to minimize the cost of its own flow. Users are atomic, in the sense that each has a nonnegligible amount of flow demand, and flows may be ...

The path, the wheelbarrow, and the bicycle inequalities have been shown by Cornuéjols, Fonlupt, and Naddef to be facet-defining for the graphical relaxation of STSP(n), the polytope of the symmetric traveling salesman problem on an n-node complete ...