Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Quadratic Cost Function x^T Q x Date: Thu, 20 May 2010 15:50:21 +0000 (UTC) Organization: Imperial College London Lines: 22 Message-ID: <ht3lnt$92i$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-03-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1274370621 9298 172.30.248.38 (20 May 2010 15:50:21 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Thu, 20 May 2010 15:50:21 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1192337 Xref: news.mathworks.com comp.soft-sys.matlab:637652 Hello, I have a (quadratic) non-linear problem of the type x^T Q x. Specifically the non-convex objective function is given by J = SUM ||x^T Qi x||^2 for i <= 3. My goal is to find arg min x, i.e. the values for the vector x. Q is a symmetric 3 x 3 matrix and x is a vector of length 3. This is why i <= 3 since we have 3 parameters (unknowns) in x. I am currently using lsqnonlin to find a solution. However I am getting trapped in local minima if I don't use a good starting guess for vector x. My question is, can I use something more 'robust' than lsqnonlin? Furthermore is there actually a global minimum in my problem? What would be the best way to find it? Many thanks.