Mathematical Programming

, Volume 133, Issue 1–2, pp 227–242 | Cite as

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

Full Length Paper Series A


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.


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 


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Copyright information

© Springer and Mathematical Optimization Society 2010

Authors and Affiliations

  1. 1.Network Design Research CenterKyushu Institute of TechnologyChiyoda-ku, TokyoJapan

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