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8 papers · 2 filters
A Multidimensional Fatou Lemma for Conditional Expectations
E. Babaei, I. V. Evstigneev, K. R. Schenk-Hoppé
The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensio…
Packing of Circles on Square Flat Torus as Global Optimization of Mixed Integer Nonlinear problem
Sergey A. Smirnov, Vladimir V. Voloshinov
The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implemen…
Walrasian Equilibrium and Centralized Distributed Optimization from the point of view of Modern Convex Optimization Methods on the Example of Resource Allocation Problem
Anastasiya Ivanova, Alexander Gasnikov, Evgeni Nurminski +1
We consider the resource allocation problem and its numerical solution. The following constructions are demonstrated: 1) Walrasian price-adjustment mechanism for determining the eq…
Generalized Mirror Prox for Monotone Variational Inequalities: Universality and Inexact Oracle
Fedor Stonyakin, Alexander Gasnikov, Pavel Dvurechensky +2
We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. A…
Optimal Distributed Optimization on Slowly Time-Varying Graphs
Alexander Rogozin, César A. Uribe, Alexander Gasnikov +2
We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated…
An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
Pavel Dvurechensky, Eduard Gorbunov, Alexander Gasnikov
We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be co…