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Distributed Line Search for Multiagent Convex Optimization

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Mathematical Control Theory I

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 461))

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Abstract

This note considers multiagent systems seeking to optimize a convex aggregate function. We assume that the gradient of this function is distributed, meaning that each agent can compute its corresponding partial derivative with information about its neighbors and itself only. In such scenarios, the discrete-time implementation of the gradient descent method poses the basic challenge of determining appropriate agent stepsizes that guarantee the monotonic evolution of the objective function. We provide a distributed algorithmic solution to this problem based on the aggregation of agent stepsizes via adaptive convex combinations. Simulations illustrate our results.

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Acknowledgments

Both authors wish to thank Jon Nicolás and Alexandra Cortés-Martínez for constant inspiration and joy. This work was partially supported by grants NSF CMMI-1300272 (JC) and AFOSR-11RSL548 (SM).

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, UC San Diego, 9500 Gilman Dr, La Jolla, CA, 92093-0411, USA

    Jorge Cortés & Sonia Martínez

Authors
  1. Jorge Cortés
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  2. Sonia Martínez
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Corresponding author

Correspondence to Jorge Cortés .

Editor information

Editors and Affiliations

  1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

    M. Kanat Camlibel

  2. Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA

    A. Agung Julius

  3. Department of Electrical Engineering, Indian Institute of Technology, Chennai, Tamil Nadu, India

    Ramkrishna Pasumarthy

  4. Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands

    Jacquelien M.A. Scherpen

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Cortés, J., Martínez, S. (2015). Distributed Line Search for Multiagent Convex Optimization. In: Camlibel, M., Julius, A., Pasumarthy, R., Scherpen, J. (eds) Mathematical Control Theory I. Lecture Notes in Control and Information Sciences, vol 461. Springer, Cham. https://doi.org/10.1007/978-3-319-20988-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-20988-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20987-6

  • Online ISBN: 978-3-319-20988-3

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