2 unknown variable constraint optimization with single unknown variable objective function

hello, I am writting a code where objective function is depend on single unknown variable but constraint function is depend on 2 unknown veriables. The code look like

fun=@(a) C1.*a.^2 +C2.*a+C3;
x0=[1,1];
lb = [];
ub = [];
Aeq = [];
beq =[];
A = [];
b = [];
nonlcon =@constraintfcn;
opts = optimoptions('fmincon','Display','iter','Algorithm','sqp');
 [x_value,fval]  = fmincon( fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,opts);

Also the constraint function can be written as

 function [c,ceq] = constraintfcn(z)
    a=z(1);b=z(2);
    c = a^2 + b^2 - 1;
    ceq = [];
 end

But it gives the error lke"Nonlinear constraint function is undefined at initial point. Fmincon cannot continue." How I can resolve this problem?

Answer 1

[Matt J]

fun=@(z) C1.*z(1).^2 +C2.*z(1)+C3;

[Soumili Sen]

yah,it is working. thank you so much.

Answer 2

[Matt J]

The problem, as you've posted it, has an analytical solution, which can be obtained using

https://www.mathworks.com/matlabcentral/fileexchange/53191-quadratic-minimization-with-norm-constraint

z=trustregprob(diag([2*C1,0]) ,  [-C2;0], 1)

[Soumili Sen]

ok.. thanks