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Unformatted text preview: Math464  HW 5 Due on Thursday, Feb 18 1 Linear Optimization (Spring 2010) Brief solutions to Homework 5 1. As seen in class (in Lecture 11), there may be some change of variables when we convert a polyhedron in general form to standard form. In particular, an unrestricted variable is replaced by two nonnegative variables. This transformation inherently creates corner points. For example, the polyhedron represented by { x ∈ R 2  x 2 = 1 ,x 2 ≥ } ( x 1 unrestricted in sign) is the open horizontal line lying one unit above the xaxis. This polyhedron has no corner points. But when you convert the same to standard form, you get a positive quadrant (flat plain closed on two edges) in R 3 , with the point (0 , , 1) as a corner point (assuming x 2 is the third variable in the standard form). 2. (a) Let y be an element of the cone C . Consider the polyhedron P = { λ = ( λ 1 ,...,λ n ) ∈ R n  n X i =1 λ i A i = y , λ i ≥ } ....
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 Spring '10
 Bertsekas
 Optimization, Standard form, Trigraph, Elementary algebra, Empty set

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