Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

Notarnicola, Ivano; Notarstefano, Giuseppe

doi:10.1109/tcns.2019.2925267

Cited by 67 publications

(97 citation statements)

References 34 publications

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“…In [29,30], primaldual approaches are proposed but they need a diminishing step-size to achieve convergence. In [31,32] distributed dual subgradient algorithms are proposed, in [33] the dual problem is tackled by means of consensus-ADMM and proximal operators, while an alternative approach based on successive duality steps has been investigated in [34]; however, all these algorithms typically exhibit a slow convergence rate for the local decision variables. The tracking mechanism has been also employed in [35] to solve constraint-coupled problems based on an augmented Lagrangian approach for a continuous time setting, but the considered set-up does not allow for nonsmooth costs and local constraints.…”

Section: Introductionmentioning

confidence: 99%

Tracking-ADMM for distributed constraint-coupled optimization

et al. 2020

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We consider constraint-coupled optimization problems in which agents of a network aim to cooperatively minimize the sum of local objective functions subject to individual constraints and a common linear coupling constraint. We propose a novel optimization algorithm that embeds a dynamic average consensus protocol in the parallel Alternating Direction Method of Multipliers (ADMM) to design a fully distributed scheme for the considered set-up. The dynamic average mechanism allows agents to track the time-varying coupling constraint violation (at the current solution estimates). The tracked version of the constraint violation is then used to update local dual variables in a consensus-based scheme mimicking a parallel ADMM step. Under convexity, we prove that all limit points of the agents' primal solution estimates form an optimal solution of the constraint-coupled (primal) problem. The result is proved by means of a Lyapunov-based analysis simultaneously showing consensus of the dual estimates to a dual optimal solution, convergence of the tracking scheme and asymptotic optimality of primal iterates. A numerical study on optimal charging schedule of plug-in electric vehicles corroborates the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Tracking-ADMM for distributed constraint-coupled optimization

et al. 2020

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“…Following the approach proposed in [9], we can derive a distributed algorithm to solve (2) by combining a (distributed) primal decomposition method with a relaxation approach. The algorithm reads as follows.…”

Section: Distributed Primal Decomposition Methods For Lp Solution Overmentioning

confidence: 99%

“…Several works as, e.g., [3], investigate a simplified set-up without local constraints, so that Y i ≡ R S . Recently, in [9] a methodology to overcome this issue has been proposed. We will pursue the same idea to devise a distributed primal decomposition approach for (2), that will act as a building block for our distributed algorithm.…”

Section: Primal Decompositionmentioning

confidence: 99%

“…In [7] the convergence rate of a distributed algorithm for the minimization of a common cost under a resource constraint is established. Distributed algorithms for constraint-coupled problems have been proposed in [8,9]. Second, we review parallel and distributed algorithms for MILPs.…”

Section: Introductionmentioning

confidence: 99%

“…It is based on a relaxation approach combined with a distributed primal decomposition scheme. Although the new algorithm strongly relies on the scheme proposed in [9], it represents a contribution per se. Indeed, we give a new insightful interpretation as a primal decomposition scheme with distributed negotiation among the agents of optimal local allocations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Camisa

Notarnicola

Notarstefano

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology. * This result is part of a project that has received funding

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Composite optimization with coupling constraints via dual proximal gradient method with applications to asynchronous networks

Wang

2022

Intl J Robust & Nonlinear

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In this article, we consider solving a composite optimization problem with affine coupling constraints in a multi-agent network based on proximal gradient method. In this problem, all the agents jointly minimize the sum of individual cost functions composed of smooth and possibly non-smooth parts. To this end, we derive the dual problem by the concept of Fenchel conjugate, which gives rise to the dual proximal gradient (DPG) algorithm by allowing for the asymmetric individual interpretations of the coupling constraints. Then, an asynchronous DPG (Asyn-DPG) algorithm is proposed for the asynchronous networks with heterogeneous step-sizes and communication delays. For both the two algorithms, if the non-smooth parts of the objective functions are simple-structured, we only need to update dual variables by some simple operations, accounting for the reduction of the overall computational complexity. Analytical convergence rate of the proposed algorithms is derived and their efficacy is verified by solving a social welfare optimization problem of electricity market in the numerical simulation.

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Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

Cited by 67 publications

References 34 publications

Tracking-ADMM for distributed constraint-coupled optimization

Tracking-ADMM for distributed constraint-coupled optimization

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Composite optimization with coupling constraints via dual proximal gradient method with applications to asynchronous networks

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