fmincon or linprog use in minimization?

Hi community,

As I am busy trying to optimize the function I encouter quite some difficulties. As I am not certain which optimization function to use( fmincon or linprog)? The letters are vectors and A is a m*n matrix. I am trying to optimize the values of Z & Y. In which antother problem arises as well, since z and y have different dimensions. Z is a 1x1 vector ( a number) and Y is a 2x1 vector. Does someone has a tip on which function to use and how to deal with the dimensional problems of the decision variables? Thankyou

min (l-q).'*z-s.'*y

s.t. y=x-A.'*z

0<z<d , y>0

[Torsten]

x, A, l, q and s are given ?

Answer 1

[Torsten]

l = 0.25;
q = 2; 
s = 1; 
A = 1;
x = 20;
d = 15;
f= [-s, l-q];
Aeq = [1, A];
beq = x;
lb = [0, 0];
ub = [Inf, d];
sol = linprog(f,[],[],Aeq,beq,lb,ub);
y = sol(1)
z = sol(2)

[bus14]

thank you a lot, one question that remains is how you came to the formulation of Aeq[1, A] and beq=x as for me it is vague how Aeq and beq are constructed from the given constraint.

[Torsten]

1*y + A*z = x <-> [1, A]*[y;z] = x <-> Aeq*[y;z] = beq

Answer 2

[bus14]

for the first instance my goal is to let the optimization problem work with the following values for x,A,l,q

L=[0.25]

Q=[2 ]

S=[1 ]

A= [1]

X= [20]

Answer 3

[bus14]

thank you a lot, so linprog is indeed the one to use as my objective function is a linear function.