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Distributed continuous‐time constrained convex optimization with general time‐varying cost functions
Author(s) -
Huang Bomin,
Zou Yao,
Meng Ziyang
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5383
Subject(s) - mathematical optimization , term (time) , constraint (computer aided design) , optimization problem , regular polygon , convex optimization , convex function , mathematics , set (abstract data type) , projection (relational algebra) , computer science , trajectory , feasible region , topology (electrical circuits) , algorithm , combinatorics , physics , geometry , quantum mechanics , astronomy , programming language
The distributed time‐varying constrained convex optimization problem over a connected undirected network topology is studied in this article. The proposed distributed optimization algorithm is composed of a projection map term, a consensus term, and a gradient term, and is feasible for any initial condition. We first show that the states of the optimization algorithm uniformly converge to a neighborhood of the constraint set while an approximate global consensus is achieved. Then the states are proven to uniformly converge to a neighborhood of the time‐varying optimal trajectory. The theoretical results are validated by some simulations.