Re: convex optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg92385] Re: convex optimization
• From: Yves Klett <yves.klett at googlemail.com>
• Date: Tue, 30 Sep 2008 07:34:57 -0400 (EDT)
• References: <gbmpr7\$i7u\$1@smc.vnet.net>

```Art,

why not have a look at:

http://reference.wolfram.com/mathematica/guide/Optimization.html
or
guide/Optimization in the Documentation Center?

For several different (both symbolic and numerical) optimization
problems I encountered the functionality out of the box worked fine.

Regards,
Yves

artg schrieb:
> What is the range of Mathematica's functionality in 'convex optimization' (as
> defined on wikipedia). Many convex optimization problems can be very
> concisely stated in Mathematica. Does it have SDP and 2nd-order cone
> programs or is it necessary to purchase an addon package?
>
> I just tried and was surprised it solved this sparse approximation problem:
>
> n = 100; m = 200;
> A = RandomReal[NormalDistribution[0, 1], {n, m}];
> b = RandomReal[NormalDistribution[0, 1], n];
> xs = Array[x, m];
>
> res = NMinimize[{Norm[xs, 1], A.xs == b}, xs];
> soln = Flatten[xs /. res[[2]]];
>
> Total at Chop[A.soln - b] == 0
> True

```

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