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Wireless networks routing: Approaches

reactive & proactive approaches being standardized optimization approach provably optimal properties routing for delay/disruption tolerant networks A different paradigm other approaches cross-layer design, network coding, …. Wireless networks routing: Approaches.

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Wireless networks routing: Approaches

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  1. reactive & proactive approaches being standardized optimization approach provably optimal properties routing for delay/disruption tolerant networks A different paradigm other approaches cross-layer design, network coding, … Wireless networks routing: Approaches

  2. Optimization-based approach • Optimization metrics • Energy consideration • Minimum energy routing • Maximum lifetime routing • (function of) throughput • Joint considerations • Routing & resource allocation • Routing & sensing

  3. Solving optimization problem • Problem specific • A very common approach • Dual decomposition: naturally renders distributed algorithms • Only describe one representative paper • L. Xiao, M. Johansson, and S. Boyd, Simultaneous Routing and Resource Allocation via Dual Decomposition, IEEE Transactions on Communications, 52(7):1136-1144, July 2004. • Goals: how to formulate optimization problem; solve convex optimization through duality

  4. A primer on solving convex optimization through duality

  5. are convex functions. Convex optimization problem in standard form

  6. The Lagrangian

  7. The Lagrange dual function Important property: p*: optimal value of the original problem.

  8. The Lagrange dual problem • What is the best lower bound that can be obtained from the Lagrange dual function? This is the dual problem. The original problem is called primal problem.

  9. Weak & strict duality • Weak duality d*: optimal value of the dual problem. p*: optimal value of the primary problem. Optimal duality gap: • Strong duality

  10. convex functions. A variant of convex optimization problem f0: concave function.

  11. The Lagrangian for the variant

  12. The Lagrange dual function for the variant Important property: p*: optimal value of the original problem.

  13. The Lagrange dual problem for the variant • What is the best upper bound that can be obtained from the Lagrange dual function?

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