lecture5 - Main Points of this Lecture Def: basic feasible...

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e62: lecture 4 29/09/10 Main Points of this 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 4 29/09/10 Basic Feasible Solutions Polytope: Def. Linearly independent constraints Def. Basic solution = intersection of N lin. indep. boundaries Combinatorial representation Def. Basic feasible solution = basic solution that is feasible Thm: there are a ±nite number of BFSs 2 P = { x ∈± N | Ax b } 12 24 - 11 51 ± x 1 x 2 ² b 1 b 2 b 3 b 4
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e62: lecture 4 29/09/10 Convexity Def: w is a convex combination of u and v if Def: a set is convex if it includes all convex combinations of its elements Thm:
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This note was uploaded on 07/29/2011 for the course MS&E 111 at Stanford.

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lecture5 - Main Points of this Lecture Def: basic feasible...

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