DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs
This paper develops a fast distributed algorithm, termed DEXTRA, to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Exis...
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| Published in | IEEE transactions on automatic control Vol. 62; no. 10; pp. 4980 - 4993 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.10.2017
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| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper develops a fast distributed algorithm, termed DEXTRA, to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Existing algorithms solve the problem restricted to directed graphs with convergence √ rates of O(ln k/ √k) for general convex objective functions and O(ln k/k) when the objective functions are strongly convex, where k is the number of iterations. We show that, with the appropriate step-size, DEXTRA converges at a linear rate O(τ k ) for 0 <; τ <; 1, given that the objective functions are restricted strongly convex. The implementation of DEXTRA requires each agent to know its local out-degree. Simulation examples further illustrate our findings. |
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| AbstractList | This paper develops a fast distributed algorithm, termed DEXTRA, to solve the optimization problem when n agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Existing algorithms solve the problem restricted to directed graphs with convergence √ rates of O(ln k/ √k) for general convex objective functions and O(ln k/k) when the objective functions are strongly convex, where k is the number of iterations. We show that, with the appropriate step-size, DEXTRA converges at a linear rate O(τ k ) for 0 <; τ <; 1, given that the objective functions are restricted strongly convex. The implementation of DEXTRA requires each agent to know its local out-degree. Simulation examples further illustrate our findings. |
| Author | Chenguang Xi Khan, Usman A. |
| Author_xml | – sequence: 1 surname: Chenguang Xi fullname: Chenguang Xi email: chenguang.xi@tufts.edu organization: Dept. of Electr. & Comput. Eng., Tufts Univ., Medford, MA, USA – sequence: 2 givenname: Usman A. surname: Khan fullname: Khan, Usman A. email: khan@ece.tufts.edu organization: Dept. of Electr. & Comput. Eng., Tufts Univ., Medford, MA, USA |
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| SubjectTerms | Acceleration Convergence Directed graphs Distributed algorithms distributed optimization Indexes Linear programming multiagent networks Optimization Symmetric matrices |
| Title | DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs |
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