Nonlinear constraint optimization gradient

Hello community, reached the end of the line with this... would appreciate your advice with this optimization.

Functions: One nonlinear to maximize and one nonlinear step function as a constraint

1) max: u(y,x) = y-0.6x^2

2) Constraints:

max(0,1-3(x-1)^2); if x<1

2-(x-2)^2; if 1<=x<=2

2; if 2<x

Objective function:

function [f,gradf] = objfungrad(x)
f = 0.6*x.^2;           
% Gradient of the objective function:
if nargout>1
 gradf = [f + 1.2*x];
end

Constraint:

function [c,ceq,DC,DCeq] = confungrad(x)
c1 = -1+(3*(x-1).^2); % Inequality constraints 
c2 = -2+(x-2).^2;
%nonlinear equality constraints
ceq=[];
% Gradient of the constraints:
if nargout > 0
  DC= [6*x+6;
      2*x+4];
  DCeq = [];
end

Solution:

x0 = [0.1 0.1];            % Starting guess 
options = optimoptions(@fmincon,'Algorithm','sqp');
options = optimoptions(options,'SpecifyObjectiveGradient',true,'SpecifyConstraintGradient',true);
lb = []; ub = [];  
[x,fval] = fmincon(@objfungrad,x0,[],[],[],[],[],[],...
  @confungrad,options);

Errors:

>> Solution
Error using fmincon (line 608)
Supplied objective function must return a scalar value.
Error in Solution (line 5)
[x,fval] = fmincon(@objfungrad,x0,[],[],[],[],[],[],...

Your guidance is greatly appreciated. I have tried this a myriad of ways and specifications and am at a loss. Thank you!!

Graph of objective and constraint functions. Note: x==z; q==y

%

[Hendrik van Gils]

Your objective function returns a vector, you could try to use:

function [f,gradf] = objfungrad(x)

f = x.'*x; % the 0.6 doesn't change the location of the optimum, but you can add it if you want.

% Gradient of the objective function:

if nargout>1

gradf = [f + 1.2*x];

end