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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)
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"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