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Distributed line search for multi-agent convex optimization
J. Cortés, S. Martínez
Mathematical Control Theory I. Nonlinear and Hybrid Control Systems, dedicated to the 60th birthday of Arjan van der Schaft, ed. M. K. Camlibel, A. Julius, R. Pasumarthy, and J. M. A. Scherpen, Lecture Notes in Control and Information Sciences, vol. 461, Springer-Verlag, 2015, pp. 95-110

Abstract

This note considers multi-agent 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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