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13
Stochastic first order methods in smooth convex optimization
, 2011
"... In this paper, we are interested in the development of efficient firstorder methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the firstorder information. First, we consider the Stochastic Primal Gradient method, which ..."
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In this paper, we are interested in the development of efficient firstorder methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the firstorder information. First, we consider the Stochastic Primal Gradient method, which is nothing else but the Mirror Descent SA method applied to a smooth function and we develop new practical and efficient stepsizes policies. Based on the machinery of estimates sequences functions, we develop also two new methods, a Stochastic Dual Gradient Method and an accelerated Stochastic Fast Gradient Method. Convergence rates on average, probabilities of large deviations and accuracy certificates are studied. All of these methods are designed in order to decrease the effect of the stochastic noise at an unimprovable rate and to be easily implementable in practice (the practical efficiency of our method is confirmed by numerical experiments). Furthermore, the biased case, when the oracle is not
Sustainable migration policies
"... This paper considers whether countries might mutually agree a policy of allowing free movement of workers. For the countries to agree, the short run costs must outweighed by the long term benefits that result from better labor market flexibility and income smoothing. We show that such policies are l ..."
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This paper considers whether countries might mutually agree a policy of allowing free movement of workers. For the countries to agree, the short run costs must outweighed by the long term benefits that result from better labor market flexibility and income smoothing. We show that such policies are less likely to be adopted for less risk averse workers and for countries that trade more. More surprisingly we find that some congestion costs can help. This reverses the conventional wisdom that congestion costs tend to inhibit free migration policies.
Stable and efficient coalitional networks
, 2011
"... We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each ..."
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Cited by 6 (0 self)
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We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with her coalition members and with individuals outside her coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concepts of strong stability and of contractual stability. Contractual stability imposes that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. Requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and efficiency. Moreover, this new framework can provide in sights that one cannot obtain if
Oligopolistic competition with general complementarities
, 2011
"... In this paper we extend the basic model of Cournot competition to the case where both the demand function and the cost functions of each firm depend on the amounts produced by competitors. In this modified setting, proving existence of equilibria becomes harder. We develop a generalization of the th ..."
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In this paper we extend the basic model of Cournot competition to the case where both the demand function and the cost functions of each firm depend on the amounts produced by competitors. In this modified setting, proving existence of equilibria becomes harder. We develop a generalization of the theory of supermodular games in the context where individual decision variables take values in a totally ordered set to prove existence of equilibria in this generalized Cournot setting.
On the hop constrained Steiner tree problem with multiple root nodes
 Proceedings of the 2nd International Symposium on Combinatorial Optimization, volume 7422 of LNCS
, 2012
"... Abstract. We consider a new network design problem that generalizes the Hop and Diameter Constrained Minimum Spanning and Steiner Tree Problem as follows: given an edgeweighted undirected graph whose nodes are partitioned into a set of root nodes, a set of terminals and a set of potential Steiner ..."
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Abstract. We consider a new network design problem that generalizes the Hop and Diameter Constrained Minimum Spanning and Steiner Tree Problem as follows: given an edgeweighted undirected graph whose nodes are partitioned into a set of root nodes, a set of terminals and a set of potential Steiner nodes, find a minimumweight subtree that spans all the roots and terminals so that the number of hops between each relevant node and an arbitrary root does not exceed a given hop limit H. The set of relevant nodes may be equal to the set of terminals, or to the union of terminals and root nodes. This paper presents theoretical and computational comparisons of flowbased vs. pathbased mixed integer programming models for this problem. Disaggregation by roots is used to improve the quality of lower bounds of both models. To solve the problem to optimality, we implement branchandprice algorithms for all proposed formulations. Our computational results show that the branchandprice approaches based on path formulations outperform the flow formulations if the hop limit is not too loose. 1
Dynamic programming driven memetic search for the steiner tree problem with revenues, budget, and hop constraints
 INFORMS JOURNAL ON COMPUTING
, 2015
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Optimal taxation in the presence of a congested public good and an application to transport policy
, 2011
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IP modeling of the survivable hop constrained connected facility location problem
"... Abstract We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hoplength constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root fac ..."
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Abstract We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hoplength constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root facility, a set of optional Steiner nodes, and the set of the potential connections among these nodes, that task is to decide which facilities to open, how to assign the clients to the open facilities, and how to interconnect the open facilities in such a way, that the resulting network contains at least λ edgedisjoint paths, each containing at most H edges, between the root and each open facility and that the total cost for opening facilities and installing connections is minimal. We study two IP models for this problem and present a branchandcut algorithm based on Benders decomposition for finding its solution. Finally, we report computational results.