asst3 - CO 355 Mathematical Optimization (Fall 2010)...

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CO 355 Mathematical Optimization (Fall 2010) Assignment 3 Due: Tuesday, November 2nd, in class. Policy. No collaboration is allowed. You may use the course notes / textbook and the lecture slides, but please be very specific when using citing results found there. (Don’t just say “from some claim in class we know. ...”.) Every other resource that you might stumble upon must be properly referenced. You are welcome to seek help from the current instructor and TAs for CO 355. Let C be a non-empty convex set. Let A be an affine space such that C A and dim A = dim C . In fact, A is unique, and it is called the affine hull of C . We say that a point x C is a relative interior point of C if there exists a closed ball B ( x,± ) centered at x of radius ± > 0 such that B ( x,± ) A C . (In other words, y A and k x - y k ≤ ± jointly imply y C .) The set of all relative interior points of C is denoted ri( C ). The relative interior is often very useful because ri( C ) is non-empty and convex (assuming
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asst3 - CO 355 Mathematical Optimization (Fall 2010)...

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