Fsolve : I want to give a condition which is something should be bigger than something, how can I do it?

I am solving one objective function.

And one of the conditions is that something is bigger than something.

I can I write this condition in fsolve function?

pl=@(E) [
  g/E(1)+G0(E)+rho*G1(E)*b/(1+a*b)-b/(1+a*b)*(g/E(2)+b*G1(E));
  R-E(1)-E(2)
  ];
P=fsolve(pl, E0);

Here I want to give two more condition such as

pl=@(E) [
  g/E(1)+G0(E)+rho*G1(E)*b/(1+a*b)>0
  b/(1+a*b)*(g/E(2)+b*G1(E))>0

How can I do this?

Answer 1

[Walter Roberson]

In order to express that a > b, you can reframe that as a + c = b where c is constrained to be positive.

However, it may perhaps be difficult to express strictly positive, as a lot of the routines are set up for constraints >= 0 rather than > 0

Answer 2

[Sargondjani]

you could also use fmincon. have a look at it

then you have to make the objective pl^2, and you can supply the constraints separately

[Walter Roberson]

If pl(E).^2 is the objective, then pl(E) and -pl(E) become equally plausible, which does not help in requiring pl(E) > 0 .

[Sargondjani]

i think there is some confusion...

his first 'pl' is the objective

his second 'pl' (should have gotten another name) are the constraints, which are the first and second part of the the objective function (both required >0).

when the latter 2 are inserted as constraints in fmincon, the algorithm will solve this properly...