# How to set lower bound lb as a function of optimization variable.

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Sol Elec on 10 May 2024
Commented: Sol Elec on 12 May 2024
I am solving one optimization using fmincon. Objectives function is a variable of x1,x2,x3.
B= 0; c =[ 0 0.1736 0.0693; 0 0 0.1736]
c = 2x3
0 0.1736 0.0693 0 0 0.1736
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l_op = 6.3247;
rho = 1.225;
R=37.5; A = pi * R^2;
Z = 8;
n =3;
k= 0.1;
Th = sym('Th', [1, n]);
x = sym('x', [1, n]);
Lam = sym('Lam', [1, n]);
Pt = sym('P_opt', [1, n]);
Per = sym('Per', [1, n]);
z = sym('z', [1, n]);
z(1) = Z;
for i = 1:n
if i > 1
term_sum = 0;
for j = 1:i-1
term_sum = term_sum + ((1 - sqrt(1 - Th(j))) * c(j, i))^2;
end
z(i) = Z * (1 - sqrt(term_sum));
end
Lam(i) = (x(i) * R) / z(i);
Th(i) = (0.000086 * B - 0.0026) * Lam(i)^3 + (-0.0018 * B + 0.0481) * Lam(i)^2 + (0.008 * B - 0.165) * Lam(i) + (-0.0116 * B + 0.3);
Per(i) = 0.22 * (116 / (Lam(i) + 0.08 * B) - 4.06 / (B^3 + 1) - 0.4 * B - 5) * exp(-12.5 / (Lam(i) + 0.08 * B) + 0.4375 / (B^3 + 1));
Pt(i) = 0.5 * rho * A * Per(i) * z(i)^3;
end
objective = -sum(Pt)
objective =
Obj = matlabFunction(objective, 'Vars', {x});
% Lower and upper bounds
lb = 0.1687 * z(i) % z(i) is a function of x(i) *corrected
Unrecognized function or variable 'v'.
ub = 1.6867*ones(1,n);
% Initial guess
x0 = ones(1,n);
% Constraints
Aeq = [];
beq = [];
% Optimization using fmincon
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'interior-point');
% % Optimize the objective function
[x_opt, fval_opt] = fmincon(Obj, x0, [], [], Aeq, beq, lb, ub, [], options);
In my optimization lower bound of the optimization is a function of optimaztion variables. How can I solve it? fmincon can be able to do it or another optimization tools can be chosen?
John D'Errico on 10 May 2024
That is not a "bound" constraint. It is an inequality constraint.
Sol Elec on 10 May 2024
How can I modify it? Becuase z(i) is the function of x(i)? @John D'Errico

Torsten on 10 May 2024
Edited: Torsten on 10 May 2024
Use function "nonlcon" to define nonlinear equality and inequality constraints.
If v(i) depends linearly on the solution variable vector x, you could also use A and b in the call to "fmincon":
Torsten on 12 May 2024
Edited: Torsten on 12 May 2024
I just saw that z is defined in your loop. In this case, simply use
zfun = matlabFunction(z,'Vars',{x})
nonlcon = @(x)deal(0.1687*zfun(x)-x,[])
Here it is assumed that the x passed from "fmincon" to "nonlcon" is a row vector.
Sol Elec on 12 May 2024
Thanks a lot for your valuable input regarding this. @Torsten @Walter Roberson.