Unformatted text preview: ž (1) minimize Ax âˆ’ b 2
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1âˆ’ x âˆž (2) and the very closely related problem In both problems, the variable is x âˆˆ Rn , and the data are A âˆˆ RmÃ—n and b âˆˆ Rm . Note that
the only diï¬€erence between problem (1) and (2) is the square in the numerator. In both problems,
the constraint x âˆž < 1 is implicit. You can assume that b âˆˆ R(A), in which case the constraint
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x âˆž < 1 can be replaced with x âˆž â‰¤ 1.
Answer the following two questions, for each of the two problems. (So you will answer four questions
all together.) (a) Is the problem, exactly as stated (and for all problem data), convex? If not, is it quasiconvex?
Justify your answer.
(b) Explain how to solve the problem. Your method can involve an SDP solver, an SOCP solver,
an LP solver, or any combination. You can include a oneparameter bisection, if necessary.
(For example, you can solve the problem by bisection on a parameter, where each iteration
consists of solving an SOCP feasibility problem.)
Give the best method you can. In judging best, we...
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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 Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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