I would like to solve the following compound optimization problem in MATLAB:
min (Ax-a), min (Bx-b), min (Cx-c)
subject to Dx=d and x>=0, where a,b,c,d,A,B,C,D are given.
First of all, I don't know how to set up the above problem, should I write
min(Ax-a)^2+min(Bx-b)^2+min(Cx-c)^2, s.t. Dx=d and x>=0
Is this the best formulation of such problem? The second question is, should I use quadprog or are there other more suitable routines in MATLAB?