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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.
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 graph. We show that these inequalities, and...
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 split over different routes. The total cost...
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 ⫅ ℝ n that converge to P in n steps. Many such methods have been shown to require n steps in the worst case. In this paper, we...
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 wider range of utility functions than has been...
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 oligopolists can reduce efficiency, measured as...
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, it is shown that whenever U n tends to...
The marriage model due to Gale and Shapley (Gale, D., L. S. Shapley. 1962. College admissions and the stability of marriage. Amer. Math. Monthly 69 9–15) and the assignment model due to Shapley and Shubik (Shapley, L. S., M. Shubik. 1972. The assignment game I: The core. Internat. J. Game...
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 communicating MDPs. The unicost MDPs are...
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 results.
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