Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Question on the derivate /calculus of a 2-norm matrix . Thanks a lot Date: Mon, 26 Jul 2010 03:33:05 +0000 (UTC) Organization: Anhui University Lines: 23 Message-ID: <i2ivlh$dka$1@fred.mathworks.com> References: <i2he90$21a$1@fred.mathworks.com> <i2iran$deb$1@fred.mathworks.com> <i2isv7$pi7$1@fred.mathworks.com> <i2itv4$rr8$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-03-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1280115185 13962 172.30.248.38 (26 Jul 2010 03:33:05 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Mon, 26 Jul 2010 03:33:05 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 2419503 Xref: news.mathworks.com comp.soft-sys.matlab:656064 "Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i2itv4$rr8$1@fred.mathworks.com>... > "Antony " <mutang.bing@gmail.com> wrote in message <i2isv7$pi7$1@fred.mathworks.com>... > > > But, according to the chain rule, I may apply it to f(X)=||KX-B||^0.6 and obtain the result of the derivate as 0.6*K.'*(K*X-B)^{-0.4}? > ====================== > > No, this wouldn't be the correct expression. From my last post, I get, after some simplification > > Gradient = 0.6*K.'*(K*X-B)/||K*X-B||^(1.4) > > > >This result seems rather complex for some numerical optimization. > ======================= > > Well, your objective function f(X)=||KX-B||^0.6 is unusually complex... > > For one thing, this function is not differentiable at points where K*X=B, which means that if the minimum lies there, you cannot use gradient-based approaches to find it. Dear Matt, thank a lot for your time in my question. I appreciate your help! I understand the difficulties of such type of optimization problems now. This might be the reason that papers always figure out another efficient solutions to such type of non-convex problems. Thanks again! Also, thanks a lot for all other guys' kind and patient helps, especially to Roger Stafford and Brian Borchers. Antony