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Topic: Non-linear optimization
Replies: 32   Last Post: Mar 8, 2013 2:22 AM

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Toan Cao

Posts: 52
Registered: 10/15/10
Re: Non-linear optimization
Posted: Mar 5, 2013 12:44 PM
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"Steven_Lord" <slord@mathworks.com> wrote in message <kh52bl$jbp$1@newscl01ah.mathworks.com>...
>
>
> "Toan Cao" <toancv3010@gmail.com> wrote in message
> news:kh3p76$mhd$1@newscl01ah.mathworks.com...

> > "Steven_Lord" <slord@mathworks.com> wrote in message
> > <kh2ni9$9ar$1@newscl01ah.mathworks.com>...

>
> *snip*
>

> > As i know, Levenberg-Marquardt, Gauss-Newton methods use f(x) to calculate
> > the Jacobian matrix. If i just have F(x) ( not f(x) ), how does
> > optimization solvers compute this matrix? Can you explain for me the way
> > that the solvers implement ?

>
> I believe the documentation for Optimization Toolbox and Global Optimization
> Toolbox describe the algorithms the functions in those two toolboxes use in
> some detail.
>

> > Actually, i need to understand more deeply and hope to modify somethings
> > for my specific function.

>
> Why? What's your application?
>
> --
> Steve Lord
> slord@mathworks.com
> To contact Technical Support use the Contact Us link on
> http://www.mathworks.com

Hi Steve Lord,

I will explain more detail about my cost function and hope to receive your suggestion.
Given two 3D point clouds (source point cloud (SPC) and target point cloud (TPC)). I would like to move each point of SPC to be coincide with each corresponding point of TPC.
Each movement of each point of SPC is described by a Rotation matrix Ri and a translation vector Ti.
Rotation matrix Ri is constrained:
Rot(Ri)= (C1.C2)^2 + (C1.C3)^2 + (C2.C3)^2 +(C1.C1 -1)^2 +(C2.C2 -1)^2 + (C3.C3 -1)^2, where C1, C2, C3 are 3x1 column vectors of Ri.
Given m points in SPC, the first term of cost function is: Sum(Rot(Ri)) where i =1:m
If we call a point in SPC is Vi, its corresponding point in TPC is Ui, its transformed point is V'i. So, the second term of cost function is: Sum((V'i - Ui)^2), i=1:m
Finally, my cost function is F = Sum(Rot(Ri)) +Sum((V'i - Ui)^2), i=1:m

Now, i want to find all Ci of Rotation matrices Ri as well all elements of translation vectors Ti. What should i do to obtain local minimum value of this function ?
Looking forward to your reply.
Thanks in advance
Toan







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