lecture6 - Summary of Previous Lecture Def: vertex of a...

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e62: lecture 6 4/10/10 Summary of Previous Lecture Def: basic feasible solution = feasible solution at intersection of N linearly independent constraint boundaries Def: vertex of a polytope = an element that is not between any others Thm: vertex = basic feasible solution Thm: there is usually a vertex that is an optimal solution 1 Concepts will be useful for analysis and algorithm development e62: lecture 6 4/10/10 In Search of an Optimal Vertex Enumerate and evaluate all vertices? 100-dimensional hypercube ! # vertices > 10 30 Simplex method Top 10 algorithms of the 20th century Local search Assess edges leaving vertex Move to an adjacent vertex Hirsch conjecture Diameter Disproved in May 2010 2 M - N e62: lecture 6 4/10/10 BFS in a Symmetric Form LP 3 max cx s . t . Ax b x 0 max [ 32 . 5 ] x 1 x 2 s . t . 4 . 44 0 06 . 67 42 . 86 36 ± x 1 x 2 ² 100 100 100 100 ± 10 01 ²± x 1 x 2 ² ± 0 0 ² car assembly truck assembly
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lecture6 - Summary of Previous Lecture Def: vertex of a...

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