
Re: Nonlinear optimization
Posted:
Mar 5, 2013 12:44 PM


"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, LevenbergMarquardt, GaussNewton 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

