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Re: How to solve this non-convex quadratically constrained quadratic programming
Posted:
Apr 18, 2012 1:34 AM
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Lucy <comtech.usa@gmail.com> wrote in message <3072521.689.1334707719706.JavaMail.geo-discussion-forums@ynmm9>...
> How to solve this quadratically constrained quadratic programming
> problem?
>
> Hi all,
>
> Could you please shed some lights on this? (Not a homework problem)
>
> I am looking for solutions to solve the following problem:
>
> max ||Xb||^2
> s.t. ||b-b 0 ||^2 <a,||b||^2=1
>
>
This might take a close look of, which essentially solves the above problem with single constraint:
http://www.mathworks.com/matlabcentral/fileexchange/27596-least-square-with-2-norm-constraint
You can start first to ignore the inequality constraint | b - b0 |^2 <= a, and solve the optimization with the spherical constraint, or the opposite minimizing =|Xb| such that |b-b0|^2=1. If the solution satisfies the (ignored) inequality, then the problem is solved.
Otherwise you might take a look at the paper referred by the FEX to see if the formulation can be twisted to your problem with two equalities:
max ||Xb||^2
s.t. ||b-b 0 ||^2 =a, ||b||^2=1
% Bruno
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