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I have the following optimization problem and I don't know how to approach it, I'm not even sure if I'd be able to get a closed form solution:
$$\min_b \|d-b\| \\ \text{s.t.} Ab < y $$ I'm trying to find the vector $b$ that is closest to the vector $d$ (known) in terms of Euclidean distance. Both $d$ and $b$ are $N$-dimensional vectors.
$A$ is an $M\times N$ matrix and is known, $y$ is an $M$-dimensional vector and is also known.
Any guidance on which optimization method I should use would be of great help.

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Square your objective and your problem becomes quadratic programming. – Rahul Aug 16 '12 at 20:43
Presumably you want $\le$ rather than $<$, otherwise there is no optimal solution. – Robert Israel Aug 16 '12 at 20:51
Thank you guys. – ca_redditor Aug 18 '12 at 4:03

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