A Regularized Saddle-Point Algorithm for (一个正规化的鞍点算法).pdf
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A Regularized Saddle-Point Algorithm for Networked Optimization
with Resource Allocation Constraints
— TECHNICAL REPORT —
This is an extended version of a paper accepted for CDC 2012 with identical title
Andrea Simonetto, Tam´as Keviczky, Mikael Johansson
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0 Abstract— We propose a regularized saddle-point algorithm make use of regularization and solve the resulting strictly
2 for convex networked optimization problems with resource convex problem via a saddle-point method. Furthermore, we
allocation constraints. Standard distributed gradient methods
g incorporate the resource allocation equality constraints di-
suffer from slow convergence and require excessive communi-
u rectly into the saddle-point iterations by extending the results
cation when applied to problems of this type. Our approach
A offers an alternative way to address these problems, and ensures of [8] (originally proposed for unconstrained problems). We
6 that each iterative update step satisfies the resource allocation derive step-size conditions that guarantee convergence of our
constraints. We derive step-size conditions under which the iterative scheme, and show how these results are linked to the
]
distributed algorithm converges geometrically to the regularized problem characteristics and the graph topology, respectively.
Y optimal value, and show how these conditions are affected by
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