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Subject: Re: How to solve this non-convex quadratically constrained quadratic programming
Date: Sun, 22 Apr 2012 16:35:09 +0000 (UTC)
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"Matt J" wrote in message <jmrdm1$oam$1@newscl01ah.mathworks.com>...
>
> So, the optimal lambda must satisfy the above polynomial eigenvalue problem. But which solution is desired?  Rearranging the original Lagrange multiplier equation 
> 
> lambda*x =H*x-g
> 
> Premultiplying by x' on both sides and using x'*x=1 again leads to
> 
> lambda =  x'*H*x-g'*x =objective
> 
> So taking the minimum/maximum solution to the polynomial eigenvalue problem is equivalent to minimizing/maximizing the objective. 
==============

I just realized that this part is wrong. The objective function is really

f(x) = 0.5*x'*H*x-g'*x 

So, it's not clear to me why we want to minimize over the admissible lambda. Oh well, I guess the Gander et al paper explains it.