Linear Programming 2015 1 Chapter 6. Large Scale Optimization.

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Presentation transcript:

Linear Programming Chapter 6. Large Scale Optimization

Linear Programming Cutting stock problem W = scrap

Linear Programming

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Cutting plane methods

Linear Programming

Dantzig-Wolfe decomposition

Linear Programming

Linear Programming

Linear Programming Decomposition algorithm

Linear Programming

Linear Programming Starting the algorithm

Linear Programming Termination and computational experience  Fast improvement in early iterations, but convergence becomes slow in the tail of the sequence. Revised simplex is more competitive in terms of running time. Suitable for large, structured problems.  Researches on improving the convergence speed. Stabilized column generation. Think in dual space. How to obtain dual optimal solution fast?  Advantages of decompositon approach also lies in the capability to handle (isolate) difficult structures in the subproblem when we consider large integer programs (e.g., constrained shortest path, robust knapsack problem type).

Linear Programming Bounds on the optimal cost

Linear Programming