TY - CHAP

T1 - Distributed bregman-distance algorithms for min-max optimization

AU - Srivastava, Kunal

AU - Nedić, Angelia

AU - Stipanović, Dušan

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We consider a min-max optimization problem over a time-varying network of computational agents, where each agent in the network has its local convex cost function which is a private knowledge of the agent. The agents want to jointly minimize the maximum cost incurred by any agent in the network, while maintaining the privacy of their objective functions. To solve the problem, we consider subgradient algorithms where each agent computes its own estimates of an optimal point based on its own cost function, and it communicates these estimates to its neighbors in the network. The algorithms employ techniques from convex optimization, stochastic approximation and averaging protocols (typically used to ensure a proper information diffusion over a network), which allow time-varying network structure. We discuss two algorithms, one based on exact-penalty approach and the other based on primal-dual Lagrangian approach, where both approaches utilize Bregman-distance functions.We establish convergence of the algorithms (with probability one) for a diminishing step-size, and demonstrate the applicability of the algorithms by considering a power allocation problem in a cellular network.

AB - We consider a min-max optimization problem over a time-varying network of computational agents, where each agent in the network has its local convex cost function which is a private knowledge of the agent. The agents want to jointly minimize the maximum cost incurred by any agent in the network, while maintaining the privacy of their objective functions. To solve the problem, we consider subgradient algorithms where each agent computes its own estimates of an optimal point based on its own cost function, and it communicates these estimates to its neighbors in the network. The algorithms employ techniques from convex optimization, stochastic approximation and averaging protocols (typically used to ensure a proper information diffusion over a network), which allow time-varying network structure. We discuss two algorithms, one based on exact-penalty approach and the other based on primal-dual Lagrangian approach, where both approaches utilize Bregman-distance functions.We establish convergence of the algorithms (with probability one) for a diminishing step-size, and demonstrate the applicability of the algorithms by considering a power allocation problem in a cellular network.

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U2 - 10.1007/978-3-642-34097-0_7

DO - 10.1007/978-3-642-34097-0_7

M3 - Chapter

AN - SCOPUS:84890067050

SN - 9783642340963

T3 - Studies in Computational Intelligence

SP - 143

EP - 174

BT - Agent-Based Optimization

PB - Springer Verlag

ER -