How to solve equation min||wij ||subject to ||Cp-Pij ||22 ≤є what function to use ?

How to solve equation min||wij ||subject to ||Cp-Pij ||22 ≤є what function to use in Matlab to solve this ?

Answer 1

[Matt J]

Is Pij the same as wij? What are the unknowns. In any case, this might be applicable

http://www.mathworks.com/matlabcentral/fileexchange/27596-least-square-with-2-norm-constraint

[Alex]

Hi Matt, wij is the sparse coefficient vector.Pij is patch of an image..

[Matt J]

And? What about my other question?

[Alex]

Min||wij ||1 s.t ||Cp wij – Pij ||22 ≤ £ Here w_ij is the unknown.Cp and Pij are the Matrices where Cp is a dictionary of photos and Pij is a patch.Can u help me out to solve this.

Answer 2

[Youssef Khmou]

hi, Alex, i had once a program called "Simplex" but i lost it, anyway the best function is linprog :

Let us take an example : you have

                                   Min f(x,y,z)=-5x-4y-6z

Subject to :

                                   x  - y  + z    <= 20
                                   3x + 2y + 4z   <= 42
                                   3x + 2y        <= 30
                                   x,y,z          >  0

Then :

 f = [-5; -4; -6];A =[1 -1  1;3  2  4;3  2  0];
 b = [20; 42; 30];
 lb=zeros(3,1);
 x=linprog(f,A,b,[],[],lb)
 Optimization terminated.

x =

    0.0000
   15.0000
    3.0000