1. Linear Programming 2015 1 Chapter 6. Large Scale Optimization

2. Linear Programming 2015 2 6.2. Cutting stock problem W = 70 17 15 scrap

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8. 8 6.3. Cutting plane methods

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10. 10 6.4. Dantzig-Wolfe decomposition

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13. Linear Programming 2015 13 Decomposition algorithm

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15. Linear Programming 2015 15 Starting the algorithm

16. Linear Programming 2015 16 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).

17. Linear Programming 2015 17 Bounds on the optimal cost

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