Solving compound linear optimization problem

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?

Answer 1

[Catalytic]

I've never heard of a compound optimization problem but maybe this will help

https://www.mathworks.com/discovery/multiobjective-optimization.html

Answer 2

[Torsten]

Look up

https://de.mathworks.com/discovery/multiobjective-optimization.html