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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: How to solve this non-convex quadratically constrained quadratic programming
Date: Wed, 18 Apr 2012 05:34:24 +0000 (UTC)
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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