SEMISMOOTH NEWTON METHOD FOR WATER - FILLING PROBLEMS WITH SUM POWER CONSTRAINT
Corresponding Author(s) : Phan Quang Nhu Anh
UED Journal of Social Sciences, Humanities and Education,
Vol. 8 No. 1 (2018): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
In this paper, we investigate the semi-smooth Newton method for water - filling problems with sum power constraint. Initially, we introduce the optimal water-filling problem - the problem from information theory. It is an optimization problem in the communication system with multiple inputs and outputs (MIMO). We also review the definition of Newton derivative and some of its properties. Then we use KKT condition to transform water-filling to solve non-smooth equation. We study Newton differentiability of non-smooth function in this equation. After that, we propose the semi-smooth Newton method for solving the non-smooth equation. The linear convergence of semi-smooth Newton method is also proven. Finally, we present numerical solution in some examples.
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