In this paper, we develop new subgradient methods for solving nonsmooth convex optimization problems. These methods are the first ones, for which the whole sequence of test points is endowed with the worst-case performance guarantees. The new methods are derived from a relaxed estimating...

We provide Frank-Wolfe (= Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly...

In this paper we suggest a new framework for constructing mathematical models of market activity. Contrary to the majority of the classical economical models (e.g. Arrow- Debreu, Walras, etc.), we get a characterization of general equilibrium of the market as a saddle point in a convex-concave...

In this paper we analyze a model of proportional representation that allows for both sincere and strategic voting. We prove that strategic voters vote only for the extreme parties in any equilibrium,if the electorate is large.

In this paper, we analyze the trade war between two large countries when the trade policy is decided through majority voting. We show how the trade war equilibrium depends on the median voter production factor relative endowment. We compare this equilibrium to the one analyzed by Johnson where...

In this note, we consider a negotiation model wherein a simultaneous voting game, which endogenizes the choice of the bargaining procedur, is introduced.

The citizen-debate approach, proposed to study the performance of representative democracies, builds on a multi-stage game where the same agents are asked whether or not to become a candidate and, successively, to vote. Consistently, the solution concept adopted in Besley and Coate (1997)...

Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To...

In this paper we extend the smoothing technique [7], [9] onto the problems of Semidefinite Optimization. For that, we develop a simple framework for estimating a Lipschitz constant for the gradient of some symmetric functions of eigenvalues of symmetric matrices. Using this technique, we can...

In this paper we study the Riemannian length of the primal central path computed with respect to the local metric defined by a self-concordant function. We show that despite to some examples, in many important situations the length of this path is quite close to the length of geodesic curves. We...