Problem with Constrained Optimization with nonlinear constraints

Hello,

I am trying to do the following constrained optimization in matlab using the fmincon and nonlinear constraint.

max μ'*x

subject to A*x ≤ b

x'*Σ*x ≤ s

μ'*x + inv(F(x)(0.05))*sqrt(x'*Σ*x) ≥ −β

-1 ≤ x ≤ 1

The x is a (3x1) matrix. The problem is that the fmincon cannot find any feasible solution that is satisfying the constraints. Is it because the x is a vector and not a scalar?

Any reply would be appreciated!

Thank you in advance, Porfyria

Answer 1

[Alan Weiss]

fmincon handles vector arguments such as x. This section of the documentation gives suggestions for dealing with the case when fmincon cannot find a feasible point.

Alan Weiss

MATLAB mathematical toolbox documentation

[Porfyria]

Hello,

Thank you for your reply. I started with linprog but the solution it gives doesn't satisfy the linear constraints. Meaning: x:(3x1)

A: ones(1,3)

b = 1

A*x ≤ b

lb = [-1; -1; -1]

ub = [1; 1; 1]

x = [-0.9993; -0.9993; -0.9993]

Am I doing something wrong?

Thank you, Porfyria

[Alan Weiss]

I'm sorry, I do not understand what you mean. For the values of A and b and x that you give,

 A*x = -2.9979 ≤ b.

And the bounds lb ≤ x ≤ ub are satisfied. So what is the problem?

Alan Weiss

MATLAB mathematical toolbox documentation