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Fixed point optimization algorithm and its application to power control in CDMA data networks

Abstract

We discuss the variational inequality problem for a continuous operator over the fixed point set of a nonexpansive mapping. One application of this problem is a power control for a direct-sequence code-division multiple-access data network. For such a power control, each user terminal has to be able to quickly transmit at an ideal power level such that it can get a sufficient signal-to-interference-plus-noise ratio and achieve the required quality of service. Iterative algorithms to solve this problem should not involve auxiliary optimization problems and complicated computations. To ensure this, we devise a fixed point optimization algorithm for the variational inequality problem and perform a convergence analysis on it. We give numerical examples of the algorithm as a power control.

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Correspondence to Hideaki Iiduka.

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Iiduka, H. Fixed point optimization algorithm and its application to power control in CDMA data networks. Math. Program. 133, 227–242 (2012). https://doi.org/10.1007/s10107-010-0427-x

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  • DOI: https://doi.org/10.1007/s10107-010-0427-x

Keywords

  • Variational inequality problem
  • Two-stage non-convex optimization problem
  • Power control
  • Firmly nonexpansive mapping
  • Fixed point
  • Utility function
  • Fixed point optimization algorithm

Mathematics Subject Classification (2000)

  • 47J25
  • 65K10
  • 91A10
  • 91A40