[R] 3D constrained nonlinear least squares fit

[S M Niaz Arifin]

Hi,
I am new to R, and am trying to solve the following optimization problem:

This is a nonlinear least squares problem. I have a set of 3D voxels. All I
need is to find a least squares fit to this data. The data model actually
represent a cube-like structure, consisting of seven straight lines. The
lines have some intersections (and at this intersection both of the
participating lines end).

Please note that I need something (some routines, maybe) that works for 3D
voxels, and to which I can feed my problem directly (ie, not feeding the
line equations separately, but together, since I have some line intersection
constraints).

(In case you need more detailed description of the problem, please view the
link
http://sites.google.com/site/niazarifin/matlab-project-images 
You'd also find a model image there.)

Thanks for your patience! Any help would be greatly appreciated.

An image of my model:

http://www.nabble.com/file/p18989155/arif_frame.jpg 
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