This paper addresses the problem of robust optimization in large-scale networks of identical processors. General convex optimization problems are considered, where uncertain constraints are distributed to the processors in the network. The processors have to compute a maximizer of a linear objective over the robustly feasible set, defined as the intersection of all locally known feasible sets. We propose a novel asynchronous algorithm, based on outer-approximations of the robustly feasible set, to solve such problems. Each processor stores a small set of linear constraints that form an outer-approximation of the robustly feasible set. Based on its locally available information and the data exchange with neighboring processors, each processor repeatedly updates its local approximation. A computational study for robust linear programming illustrates that the completion time of the algorithm depends primarily on the diameter of the communication graph and is independent of the network size.

Mathias Burger, Giuseppe Notarstefano, Frank Allgower (2012). Distributed robust optimization via Cutting-Plane Consensus. USA : IEEE [10.1109/CDC.2012.6426782].

Distributed robust optimization via Cutting-Plane Consensus

Giuseppe Notarstefano;
2012

Abstract

This paper addresses the problem of robust optimization in large-scale networks of identical processors. General convex optimization problems are considered, where uncertain constraints are distributed to the processors in the network. The processors have to compute a maximizer of a linear objective over the robustly feasible set, defined as the intersection of all locally known feasible sets. We propose a novel asynchronous algorithm, based on outer-approximations of the robustly feasible set, to solve such problems. Each processor stores a small set of linear constraints that form an outer-approximation of the robustly feasible set. Based on its locally available information and the data exchange with neighboring processors, each processor repeatedly updates its local approximation. A computational study for robust linear programming illustrates that the completion time of the algorithm depends primarily on the diameter of the communication graph and is independent of the network size.
2012
IEEE Conference on Decision and Control
7457
7463
Mathias Burger, Giuseppe Notarstefano, Frank Allgower (2012). Distributed robust optimization via Cutting-Plane Consensus. USA : IEEE [10.1109/CDC.2012.6426782].
Mathias Burger; Giuseppe Notarstefano; Frank Allgower
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/671993
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