Path: news.mathworks.com!not-for-mail From: "Bruno Luong" <b.luong@fogale.findmycountry> Newsgroups: comp.soft-sys.matlab Subject: Re: Non-linear optimization Date: Tue, 5 Mar 2013 07:26:08 +0000 (UTC) Organization: FOGALE nanotech Lines: 18 Message-ID: <kh46mg$s0t$1@newscl01ah.mathworks.com> References: <kh2m44$4eh$1@newscl01ah.mathworks.com> <kh32ds$hrn$1@newscl01ah.mathworks.com> Reply-To: "Bruno Luong" <b.luong@fogale.findmycountry> NNTP-Posting-Host: www-01-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: newscl01ah.mathworks.com 1362468368 28701 172.30.248.46 (5 Mar 2013 07:26:08 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Tue, 5 Mar 2013 07:26:08 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 390839 Xref: news.mathworks.com comp.soft-sys.matlab:790321 "Matt J" wrote in message <kh32ds$hrn$1@newscl01ah.mathworks.com>... > "Toan Cao" <toancv3010@gmail.com> wrote in message > > If you know a global lower bound on F(x), say F_low, then the minimization problem is equivalent to > > min f(x)'.f(x) > > where > > f(x)=F(x)- f_low > > So, you could apply Levenberg-Marquardt and/or Gauss-Newton to the reformulated problem. I don't think it is a good suggestion. (1) It make the code difficult to handle since f_low needs to be known. It squares the conditioning of the original problem, and thus all kinds of numerical difficulties become more prominent. When levenberg-Markquardt or pseudo-newton method is developed, f(x) is usually taken as the local Jacobian of F. And this approximation is generally known and studied. The approximation can be applied on any F (only assumed to be differentiable). Bruno