Allerton 2015 Paper Abstract

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Paper ThB3.3

Valls, Víctor (Trinity College Dublin), Leith, Douglas (Trinity College Dublin)

Dual Subgradient Methods Using Approximate Multipliers

Scheduled for presentation during the Regular Session "Optimization" (ThB3), Thursday, October 1, 2015, 11:10−11:30, Butternut

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Optimization, Distributed Computation on Networks

Abstract

We consider the subgradient method for the dual problem in convex optimisation with approximate multipliers, i.e., the subgradient used in the update of the dual variables is obtained using an approximation of the true Lagrange multipliers. This problem is interesting for optimisation problems where the exact Lagrange multipliers might not be readily accessible. For example, in distributed optimisation the exact Lagrange multipliers might not be available at the nodes due to communication delays or losses. We show that we can construct approximate primal solutions that can get arbitrarily close to the set of optima as step size alpha is reduced. Applications of the analysis include unsynchronised subgradient updates in the dual variable update and unsynchronised max-weight scheduling.

 

 

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