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S_David
#42
Apr12-11, 02:40 PM
P: 597
Ok, that is good. But what is the geometric interpretation for this? I mean, as prof. Boyd's said in the solution, a trivial way is to check that all vetrices of the rectangle lie within the polytope, where we have [tex]2^{n}[/tex] vertices, right? But, apparently, there is a much more efficient way.

Let me give example: Suppose we want to insure that all elements of a matrix is less that a constant, say c. Then it suffices to check that the min element of the matrix is less than c. I think, prof. Boyd's method resembles this thinking. I don't know, may be if the maximum difference of something and something less than b, then all vertices are less than b. However, I don't know what is this "something", and what is the geometric interpretation of it.