bv_cvxbook_extra_exercises

1 x 2 and the very closely related problem in both

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Unformatted text preview: one, and the total revenue generated by the optimal solution. Also, give the average price per unit for each activity level, i.e., the ratio of the revenue associated with an activity, to the activity level. (These numbers should 13 be between the basic and discounted prices for each activity.) Give a very brief story explaining, or at least commenting on, the solution you find. 3.5 Minimizing the ratio of convex and concave piecewise-linear functions. We consider the problem minimize maxi=1,...,m (aT x + bi ) i mini=1,...,p (cT x + di ) i subject to F x g, with variable x ∈ Rn . We assume that cT x + di > 0 and maxi=1,...,m (aT x + bi ) ≥ 0 for all x satisfying i i F x g , and that the feasible set is nonempty and bounded. This problem is quasiconvex, and can be solved using bisection, with each iteration involving a feasibility LP. Show how the problem can be solved by solving one LP, using a trick similar to one described in §4.3.2. 3.6 Two problems involving two norms. We consider the problem minimize Ax − b 1 , 1− x...
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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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