Thread: How to solve coupled optimization problem?

Hi there,

I have got a problem of solving coupled optimization problem in real application. For example,


The objective function E(a,b) contains two sets of variables need to be optimized:





Assume is a transformation matrix describing the motion of the images, and is pixel intensity of the image. And is our observation. The purpose of this is to reconstruct the motion corrected image of several scene. Essentially, we would like to optimize w.r.t both and .


For a general image reconstruction problem, the problem is linear; however, the motion introduce the nonlinearity. Therefore, the problem here is a coupled nonlinear optimization problem.


Then I have a couple of question about this:


1. Is there a efficient way to solve this kind of coupled optimization problem?


2. Is that possible to linearize the problem?


Thanks for any suggestion or giving me some reference to read please.




Thanks a lot!

Is this a discrete optimization problem? What's the size of the weight matrix ?

Originally Posted by ojones

Is this a discrete optimization problem? What's the size of the weight matrix ?

Thanks for your reply. Yes, it is.

The size of is huge but is sparse. Any ideas?

Thanks.

And what's , a scalar or a vector? What's complicating things is the dependence of the weight matrix on a parameter. Do you have any references for this type of problem?