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convex optimization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92339] convex optimization
  • From: artg <grenander at gmail.com>
  • Date: Sat, 27 Sep 2008 22:23:33 -0400 (EDT)

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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