1. A Newton consensus method for distributed optimization
- Author
-
Martin Guay
- Subjects
Hessian matrix ,0209 industrial biotechnology ,Mathematical optimization ,Optimization problem ,Computer science ,020208 electrical & electronic engineering ,MathematicsofComputing_NUMERICALANALYSIS ,Perturbation (astronomy) ,02 engineering and technology ,Derivative ,Inversion (discrete mathematics) ,Newton's method in optimization ,Consensus method ,Dual (category theory) ,symbols.namesake ,020901 industrial engineering & automation ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,symbols - Abstract
This manuscript proposes a distributed Newton seeking for the solution of distributed optimization problems with locally measured but unknown cost functions. The approach implements a Newton step for both the primal and dual problems that can be implemented in a completely decentralized fashion. Unlike existing techniques, no exchange of derivative information between agents is required. In addition, no explicit inversion of the Hessian information is required to generate the required Newton step. The local gradients and Hessians are estimated using a perturbation based extremum seeking control technique. A simulation study demonstrates the effectiveness of the technique.
- Published
- 2020
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