Path: news.mathworks.com!not-for-mail 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) Organization: FOGALE nanotech Lines: 27 Message-ID: <jmljp0$jbi$1@newscl01ah.mathworks.com> References: <3072521.689.1334707719706.JavaMail.geo-discussion-forums@ynmm9> Reply-To: "Bruno Luong" <b.luong@fogale.findmycountry> NNTP-Posting-Host: www-00-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: newscl01ah.mathworks.com 1334727264 19826 172.30.248.45 (18 Apr 2012 05:34:24 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Wed, 18 Apr 2012 05:34:24 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 390839 Xref: news.mathworks.com comp.soft-sys.matlab:764940 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