Applied Optimization Methods for Wireless Networks by Hou Y.T., Shi Y., Sherali H.D.

By Hou Y.T., Shi Y., Sherali H.D.

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For an LP problem in standard form, there is another associated LP problem called the dual problem, which is given as follows: Minimize wT b subject to AT w ≥ c, where the vector of dual variables w is unrestricted in sign [10]. , with the dual simplex method or the primal-dual algorithm [10]). Based on the duality relationship in LP theory, both the original LP and its dual LP can be solved simultaneously by standard LP techniques in polynomial time. We want to emphasize that all the variables in an LP problem should be real (continuous) variables.

In the rest of this chapter, we offer a case study on how LP can be applied to address some interesting but difficult problems from wireless sensor networks. 2 Case study: Lexicographic max-min rate allocation and node lifetime problems Consider a wireless sensor network consisting of battery-powered nodes for data collection. Although there have been significant improvements in processor design and computing, advances in battery technology still lag behind, making energy resource considerations the fundamental challenge in wireless sensor networks.

10 say that for those nodes that have already reached their LMM-optimal rates, the total energy consumed for communications has reached their initial energy provisioning. 9 are for the remaining nodes that have not yet reached their LMM-optimal rates. 7 state that, for those nodes that have not yet reached their energy constraint levels, the sum of in-coming and local data rates is equal to the out-going data rates. Note that the objective function is to maximize the additional rate δl for those nodes.

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