lecture6

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online