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4120_lecture16-F10-modified

# 4120_lecture16-F10-modified - Computational Methods for...

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Click to edit Master subtitle style Computational Methods for Management and Economics Lecture 16

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Outline LP Complexity Goal Programming
Complexity of Simplex Method Complexity of simplex – we can measure it in terms of its runtime or e.g., number of iterations performed by the simplex method – why? Practice case complexity – refers to the performance (runtime) for the kinds of problems encountered in practice: depends a lot on the particular problem; difficult to estimate;

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Complexity of Simplex Method Worst case complexity – refers to the worst performance (runtime) possible of the simplex method, over all possible linear programming Problems;
Complexity of Simplex How long does it take to solve an LP using the simplex method? Several factors: the number of functional constraints (m). The number of variables (n) The density of the matrix of technological coefficients (A)

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“Practice” Complexity of Simplex The most important factor seems to be the number of functional constraints . Computation tends to be proportional to the cube of the number of functional constraints in an LP (m3).
“Practice” Complexity of Simplex The number of variables (n) is a relatively minor factor (assuming revised simplex method) The density of the matrix of technological coefficients (A) is also a factor – the sparser the

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4120_lecture16-F10-modified - Computational Methods for...

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