How to perform minimization with fminsearch and fmincon

syms x [1 26]
syms y [1 26]
syms w [1 26]
f = 0;
for i = 1:numel(a)
    r1 = reg1(i);
    r2 = reg2(i);
    f = f + w(r2) * sqrt((x(r1)-a(i))^2 + (y(r1)-b(i))^2) - w(r1) * sqrt((x(r2)-a(i))^2 + (y(r2)-b(i))^2);
end
expr_func = matlabFunction(f, 'Vars', {[x, y, w]});

In the above code, i want to perform minimzation using fmin search. Also, how to ensure that f = f + w(r2) * sqrt((x(r1)-a(i))^2 + (y(r1)-b(i))^2) - w(r1) * sqrt((x(r2)-a(i))^2 + (y(r2)-b(i))^2) >=0

Answer 1

[Walter Roberson]

%guesses for initial conditions
x0 = linspace(-1,1,26);
y0 = linspace(-2,2,26);
w0 = linspace(-3,3,26);
xyw0 = [x0, y0, w0];

%the search
bestxyw = fminsearch(expr_fun, xyw0);
bestx = bestxyw(1:26);
besty = bestxyw(27:52);
bestw = bestxyw(53:78);

[Walter Roberson]

Ensuring that the partial expressions are >= 0.

This can be done with fmincon but not with fminsearch.

syms x [1 26]
syms y [1 26]
syms w [1 26]

sym parts [26 1]

f = sym(0);
for i = 1:numel(a)
    r1 = reg1(i);
    r2 = reg2(i);
    partial = w(r2) * sqrt((x(r1)-a(i))^2 + (y(r1)-b(i))^2) - w(r1) * sqrt((x(r2)-a(i))^2 + (y(r2)-b(i))^2);
    parts(i) = partial;
    f = f + partial;
end

expr_func = matlabFunction(f, 'Vars', {[x, y, w]});
part_func = matlabFunction(-parts, 'Vars', {[x, y, w]});

A = []; b = [];
Aeq = []; beq = [];
lb = []; ub = [];
nonlcon = part_func;

%guesses for initial conditions
x0 = linspace(-1,1,26);
y0 = linspace(-2,2,26);
w0 = linspace(-3,3,26);
xyw0 = [x0, y0, w0];
%the search
bestxyw = fmincon(expr_fun, xyw0, A, b, Aeq, beq, lb, ub, nonlcon);
bestx = bestxyw(1:26);
besty = bestxyw(27:52);
bestw = bestxyw(53:78);