[CppAD] Trying to get Sparse Hessian Calculation Faster

[einglez at terra.com.br]

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	Hi, 
	At the moment I have coupled Ipopt with CppAD in order to solve my
non-linear optimization problem. I did it and to test the performance
I am using a scalable problem. 
	When the problem is small n = 100 then things converge reasonably
fast compared with the exact hessian and jacobiam calculations. 

	On the other hand, when I set n to 1000 I simply cannot have the
results. The time required is enormous.  
	I have used two strategies, which I will expose further, but none
has performed satisfactorily. 
	Strategy 1: Use SparseHessian routine 
	Actually Ipopt requires the Hessian of the Langrangian that has
multipliers for each of the constraints and objective function
Hessian. Because of that I was not able to properly compute the
Hessian of the Langrangian at once by calling SparceHessian routine.
I believe it should be done internally. One alternative would be to
compute each of the constraint and objective function per time, but
that causes the performance to be inefficient. 
	Strategy 2: Use Fortwo routine 
	Ipopt requires the non-zero structure of the hessian, as well as its
position (irow[NonZeros] and jcol[NonZeros]. I can calculate it all
and use to specifically compute the partial derivative I want. Also I
compute each constraint and objetive function per type on the irow and
jcol nonzero points of the Hessian of the Langrangian. 

	I thought it would be quick because the problem is sparse and I
won’t need to compute the n x n space.  

	For some reason I don’t know the reason it is behaving even
slower. I suspect that Fortwo is supposed to compute over the n
forward dimension even if I don’t need then. Is that true? 
	Another idea I had is to modify Hessian to compute only the points I
know it is a non-zero position (irow, jcol). Ipopt use the tripled
format for sparse matrix computations. 
	What I actually need is some orientation to change the codes in
order to make sparse computation fast enough to make Ipopt and CppAD
coupling effective. Thanks for any help and tip. 

	I know that it is on the wish list and I would like to help with
that. 
	Regards, 
	Eduardo
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