How can I do a multi-objective and non linear optimization where the objective function is an integral with a parameter that varies

In the attached picture is an equation of Gamma. I have to find the four values (a3, a2, a1 and a0) such that Gamma_dB=20*log10(abs(Gamma)) <= -15 not only with on value of k but for all the values of k, between 12 and 83.

With the following code, I managed to find the 4-elements matrix a, but for only one value of k. How can I extend the code to do the optimization of "a" for all the values of k (12:1:83) at the same time ? Thank you.

if true
freq = 3.5d9;
epsr = 2.33;
d = 0.508d-3;
c0 = 3d8;
Z0 = 50;
ZL=5.6;
L = 49.5d-3;
k = (2*pi*freq)/(c0*sqrt(epsr));
function [ Gamma ] = fun_Gamma(k, a, zmin, zmax)
  fun = @(z, k) -0.5*exp(-2*1i*k*z).*(3*a(1)*z.^2 + 2*a(2)*z + a(3))./(a(1)*z.^3 + a(2)*z.^2 + a(3)*z + a(4));
  Gamma = 20*log10(abs(integral(@(z)fun(z, k), zmin, zmax)));
end
objfun = @(a) fun_Gamma(k, a, 0, L);
nonlcon = @(a) fun_Gamma(k, a, 0, L)+20;
nonlconfun = @(a) deal(nonlcon(a), []);
Aeq = ZL/Z0*[0 0 0 1; L^3 L^2 L 1];
beq = [Z0; ZL];
a0 = [100; 100; 100; 100];
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
[a, fval, exitflag, output] = fmincon(objfun, a0, [], [], Aeq, beq, [], [], nonlconfun, options);
end

[Torsten]

How do you want to define your objective function if you consider all values of k at the same time ?

Best wishes

Torsten.