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Routing is very important step in VLSI physical design. The aim of this research is to investigate and develop routing and strategies that use convex optimisation. It will take advantage of the important property of convex optimisation that any local minimum is a global solution of the problem. The proposed models should be able to generate a competitive optimal solution for wire-length minimisation and timing congestion also the designed and developed mathematical programming method should be effective, efficient, optimal, stable, robust, flexible, scalable, and applicable.It will be helpful to users working in VLSI Physical design and its optimisation in terms of cost, delay etc. Elaborate discussion on convex optimisation is also done. This book would be use to to other researchers working on optimisation techniques.