501. Enhanced Gradient Tracking Algorithms for Distributed Quadratic Optimization via Sparse Gain Design
- Author
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Michelangelo Bin, Lorenzo Marconi, Ivano Notarnicola, Guido Carnevale, Giuseppe Notarstefano, R. Findeisen, S. Hirche, K. Janschek, M. Mönnigmann, Carnevale G., Bin M., Notarnicola I., Marconi L., and Notarstefano G.
- Subjects
0209 industrial biotechnology ,Sequence ,021103 operations research ,Computer science ,Diagonal ,MathematicsofComputing_NUMERICALANALYSIS ,0211 other engineering and technologies ,02 engineering and technology ,Network topology ,Linear dynamical system ,Matrix (mathematics) ,Nonlinear system ,020901 industrial engineering & automation ,Control and Systems Engineering ,Distributed optimization, control for optimization, consensus optimization ,Quadratic programming ,Focus (optics) ,Algorithm - Abstract
In this paper we propose a new control-oriented design technique to enhance the algorithmic performance of the distributed gradient tracking algorithm. We focus on a scenario in which agents in a network aim to cooperatively minimize the sum of convex, quadratic cost functions depending on a common decision variable. By leveraging a recent system-theoretical reinterpretation of the considered algorithmic framework as a closed-loop linear dynamical system, the proposed approach generalizes the diagonal gain structure associated to the existing gradient tracking algorithms. Specifically, we look for closed-loop gain matrices that satisfy the sparsity constraints imposed by the network topology, without however being necessarily diagonal, as in existing gradient tracking schemes. We propose a novel procedure to compute stabilizing sparse gain matrices by solving a set of nonlinear matrix inequalities, based on the solution of a sequence of approximate linear versions of such inequalities. Numerical simulations are presented showing the enhanced performance of the proposed design compared to existing gradient tracking algorithms.
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