optimproblem does not solve an analytical equation correct

Dear Matlab,

I am using optimproblem to solve a overdetermined optimization problem. Since the results were completly wrong I tried the follow problem which has a unique solution. Also there the result is extremly wrong.

I have a rectangle, each side determined by two points. I would like to get the constant and the normal vector of each side. Therefore I set up the optimization problem as follows.

% points for each side of the rectangle
Px = [0;1]

Px = 2×1

0 1

Py = [1;1]

Py = 2×1

1 1

Qx = [1;1]

Qx = 2×1

1 1

Qy = [1;0]

Qy = 2×1

1 0

Rx = [1;0]

Rx = 2×1

1 0

Ry = [0;0]

Ry = 2×1

0 0

Sx = [0;0]

Sx = 2×1

0 0

Sy = [0;1]

Sy = 2×1

0 1

zp = zeros(size(Px)); op =  ones(size(Px));
zq = zeros(size(Qx)); oq =  ones(size(Qx));
zr = zeros(size(Rx)); or =  ones(size(Rx));
zs = zeros(size(Sx)); os =  ones(size(Sx));

A = [ op zp zp zp Px  Py
     zq oq zq zq Qy -Qx
     zr zr or zr Rx  Ry
     zs zs zs os Sy -Sx]

A = 8×6

1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 -1 0 1 0 0 0 -1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0

c1 = optimvar('c1');
c2 = optimvar('c2');
c3 = optimvar('c3');
c4 = optimvar('c4');
n1 = optimvar('n1');
n2 = optimvar('n2');
optivars = [c1; c2; c3; c4; n1; n2];
prob = optimproblem;
prob.Objective = (A*optivars).'*(A*optivars);
prob.Constraints.con1 = n1*n1 + n2*n2 == 1;
    
show(prob)

  OptimizationProblem : 

	Solve for:
       c1, c2, c3, c4, n1, n2

	minimize :
       2*c1^2 + 2*c2^2 + 2*c3^2 + 2*c4^2 + 4*n1^2 + 4*n2^2 + n1*c4 + c4*n1 + n1*c3 + c3*n1 + n1*c2 + c2*n1 + n1*c1 - 2*n2*c2 + c1*n1 - 2*c2*n2 + 2*n2*c1 + 2*c1*n2


	subject to con1:
       ((n1 .* n1) + (n2 .* n2)) == 1
     

    
init_value.c1 = -1.0;
init_value.c2 = 1.0;
init_value.c3 = 0.0;
init_value.c4 = 0.0;
init_value.n1 = 0.0;
init_value.n2 = 1.0;
    
[sol,fval,exitflag] = solve(prob, init_value);

Solving problem using fmincon.

Initial point is a local minimum that satisfies the constraints.

Optimization completed because at the initial point, the objective function is non-decreasing 
in feasible directions to within the value of the optimality tolerance, and 
constraints are satisfied to within the value of the constraint tolerance.

If I do show(prob) I get the output of the optimization problem. The equations are correct and if I solve them by hand the result is correct. So why does solve(prob,init_value) not find the solution even with the perfect inital condition? I also get 70 values for each variable (c1,c2,c3,c4,n1,n2)?

Thanks

Answer 1

[Torsten]

Works for me (see above).

Your objective must return the norm of A*x (squared), not A*x.

[Gabriel Waibel]

That was the error. Thank you very much!