Is there a name for problems like this min norm(Cx) Ax = b
where C is a matrix and norm is the maximum norm. This is kind of like a linear Programm. Could this be rewritten as linear programm? Or Any idea how you could solve this?
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2 Answers
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It's a convex program. For all you ever wanted to know, read Boyd and Vanderberghe's convex optimization. (pdf available for free on same site).
answered Apr 23, 2014 at 12:36
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Your problem can be cast as a Linear Program. Just add an extra variable $z\in \mathbb{R}$ and constraints $$ z\geq c_i^Tx ,\quad z\geq -c_i^Tx,\quad i=1,\ldots,m$$ where $c_i^T$ is the $i$-th row of $C$.
Although your problem is an LP, be careful since your problem has unbounded domain. Try to write your problem in standard form, so you can use standard methods (simplex, interior-point) for solving it.
