bv_cvxbook_extra_exercises

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Unformatted text preview: 0.5 1 4.21 Robust LP with polyhedral cost uncertainty. We consider a robust linear programming problem, with polyhedral uncertainty in the cost: minimize supc∈C cT x subject to Ax b, with variable x ∈ Rn , where C = {c | F c g }. You can think of x as the quantities of n products to buy (or sell, when xi < 0), Ax b as constraints, requirements, or limits on the available quantities, and C as giving our knowledge or assumptions about the product prices at the time we place the order. The objective is then the worst possible (i.e., largest) possible cost, given the quantities x, consistent with our knowledge of the prices. In this exercise, you will work out a tractable method for solving this problem. You can assume that C = ∅, and the inequalities Ax b are feasible. (a) Let f (x) = supc∈C cT x be the objective in the problem above. Explain why f is convex. (b) Find the dual of the problem maximize cT x subject to F c g , with variable c. (The problem data are x, F , and g .) Explain...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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