27 citations · 122 across the 30 of their papers we have counts for
36 papers
On the problem of optimal fair exchange
Alexander Kolesnikov, Svetlana Popova
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the…
Beckmann's approach to multi-item multi-bidder auctions
Alexander V. Kolesnikov, Fedor Sandomirskiy, Aleh Tsyvinski +1
We consider the problem of revenue-maximizing Bayesian auction design with several bidders having independent private values over several items. We show that it can be reduced to t…
Blaschke-Santalo inequality for many functions and geodesic barycenters of measures
Alexander V. Kolesnikov, Elisabeth M. Werner
Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke-Santalo inequality and the affine isoperimetric i…
The multistochastic Monge-Kantorovich problem
Nikita A. Gladkov, Alexander V. Kolesnikov, Alexander P. Zimin
The multistsochastic Monge--Kantorovich problem on the product of spaces is a generalization of the multimarginal Monge--Kantorovich problem. For a give…
Pinsker inequalities and related Monge-Ampère equations for log concave functions
Umut Caglar, Alexander V. Kolesnikov, Elisabeth M. Werner
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant en…
On the local version of the Log-Brunn-Minkowski conjecture and some new related geometric inequalities
Alexander V. Kolesnikov, Galyna V. Livshyts
We prove that for any semi-norm on and any symmetric convex body in \begin{equation}\label{ineq-abs2} \int_{\partial K} \frac{\|n_x\…