Distributed Robust Optimization in Networked System

In this paper, we consider a distributed robust optimization (DRO) problem, where multiple agents in a networked system cooperatively minimize a global convex objective function with respect to a global variable under the global constraints. The objective function can be represented by a sum of loca...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 47; no. 8; pp. 2321 - 2333
Main Authors: Wang, Shengnan, Li, Chunguang
Format: Journal Article
Language:English
Published: United States IEEE 01.08.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Computer simulation
Convergence
Distributed optimization
Lagrangian functions
Linear programming
Multiagent systems
networked system
Nonlinear programming
Optimization
Parameter uncertainty
Projection
robust
Robustness
Robustness (mathematics)
subgradient approach
Uncertainty
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:In this paper, we consider a distributed robust optimization (DRO) problem, where multiple agents in a networked system cooperatively minimize a global convex objective function with respect to a global variable under the global constraints. The objective function can be represented by a sum of local objective functions. The global constraints contain some uncertain parameters which are partially known, and can be characterized by some inequality constraints. After problem transformation, we adopt the Lagrangian primal-dual method to solve this problem. We prove that the primal and dual optimal solutions of the problem are restricted in some specific sets, and we give a method to construct these sets. Then, we propose a DRO algorithm to find the primal-dual optimal solutions of the Lagrangian function, which consists of a subgradient step, a projection step, and a diffusion step, and in the projection step of the algorithm, the optimized variables are projected onto the specific sets to guarantee the boundedness of the subgradients. Convergence analysis and numerical simulations verifying the performance of the proposed algorithm are then provided. Further, for nonconvex DRO problem, the corresponding approach and algorithm framework are also provided.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2016.2613129