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This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.2 pp.435-442

- Publication Date
- 2020/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2019MAP0008

- Type of Manuscript
- Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)

- Category

Naoki HAYASHI

Osaka University

Yuichi KAJIYAMA

Osaka University

Shigemasa TAKAI

Osaka University

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Naoki HAYASHI, Yuichi KAJIYAMA, Shigemasa TAKAI, "Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 2, pp. 435-442, February 2020, doi: 10.1587/transfun.2019MAP0008.

Abstract: This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019MAP0008/_p

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@ARTICLE{e103-a_2_435,

author={Naoki HAYASHI, Yuichi KAJIYAMA, Shigemasa TAKAI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions},

year={2020},

volume={E103-A},

number={2},

pages={435-442},

abstract={This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.},

keywords={},

doi={10.1587/transfun.2019MAP0008},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 435

EP - 442

AU - Naoki HAYASHI

AU - Yuichi KAJIYAMA

AU - Shigemasa TAKAI

PY - 2020

DO - 10.1587/transfun.2019MAP0008

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E103-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2020

AB - This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.

ER -