This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method of Multipliers, in which each node wakes up in an uncoordinated fashion and performs either a descent step on a local Augmented Lagrangian or an ascent step on the local multiplier vector. These two phases are regulated by a distributed logic-AND, which allows nodes to understand when the descent on the (whole) Augmented Lagrangian is sufficiently small. We show that this distributed algorithm is equivalent to a block coordinate descent algorithm for the minimization of the Augmented Lagrangian followed by an update of the whole multiplier vector. Thus, the proposed algorithm inherits the convergence properties of the Method of Multipliers.

Asynchronous Distributed Method of Multipliers for Constrained Nonconvex optimization / Farina, Francesco; Garulli, Andrea; Giannitrapani, Antonio; Notarstefano, Giuseppe. - ELETTRONICO. - (2018), pp. 8550098.2535-8550098.2540. (Intervento presentato al convegno 16th European Control Conference, ECC 2018 tenutosi a Limassol, Cyprus nel 12-15 June 2018) [10.23919/ECC.2018.8550098].

Asynchronous Distributed Method of Multipliers for Constrained Nonconvex optimization

Farina, Francesco;Notarstefano, Giuseppe
2018

Abstract

This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method of Multipliers, in which each node wakes up in an uncoordinated fashion and performs either a descent step on a local Augmented Lagrangian or an ascent step on the local multiplier vector. These two phases are regulated by a distributed logic-AND, which allows nodes to understand when the descent on the (whole) Augmented Lagrangian is sufficiently small. We show that this distributed algorithm is equivalent to a block coordinate descent algorithm for the minimization of the Augmented Lagrangian followed by an update of the whole multiplier vector. Thus, the proposed algorithm inherits the convergence properties of the Method of Multipliers.
2018
2018 European Control Conference, ECC 2018
2535
2540
Asynchronous Distributed Method of Multipliers for Constrained Nonconvex optimization / Farina, Francesco; Garulli, Andrea; Giannitrapani, Antonio; Notarstefano, Giuseppe. - ELETTRONICO. - (2018), pp. 8550098.2535-8550098.2540. (Intervento presentato al convegno 16th European Control Conference, ECC 2018 tenutosi a Limassol, Cyprus nel 12-15 June 2018) [10.23919/ECC.2018.8550098].
Farina, Francesco; Garulli, Andrea; Giannitrapani, Antonio; Notarstefano, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/661675
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