why the optimal value equals infinity

clear
close all
clc
%%
B=8e6;
taw=8e-6;
K=B/taw;
fs=7*B;
t=-taw/2:1/fs:taw/2;
freq_func=K*t;
plot(t,freq_func)

%%
phi=[];
for jj=1:length(freq_func)
    vv=(t(2)-t(1))*sum(freq_func(1:jj));
    phi=[phi vv];
end
x_t=exp(1j*2*pi*phi);
% plot(real(x_t))
x_tcorr=abs(xcorr(x_t));
x_tcorr=x_tcorr/max(x_tcorr);
[val,indx]=findpeaks(x_tcorr);
sortval=sort(val,'descend');
SLL=pow2db((sortval(2)/sortval(1))^2)

SLL = -13.4973

plot(real(x_tcorr))

plot(20*log10(x_tcorr))

%%  OPTIMIZATION
% Given data
x = x_t.';         % vector of complex numbers
N_L = 8;       % integer constant
% p = ...;         % integer constant
LPG=-2;
alpha =db2pow(-LPG);     % positive scalar constant
beta =[449 443.111 389.596 323.947 243.949 158.551 76.6573 5.99828];% 1:1:2*N_L;      % vector of positive scalar constants
B=fliplr(beta);
beta=[B beta];
% lambda = ...;    % cell array of complex vectors
N=length(x);
colsig= [flipud(x); zeros(N-1,1)];
A=zeros(2*N-1,N);
for i=1:N
    A(:,i)=colsig;
    colsig=circshift(colsig,1);
end
W=A([N-7 N-6 N-5 N-4 N-3 N-2 N-1  N  N+1 N+2 N+3 N+4 N+5 N+6 N+7],:);
A([N-7 N-6 N-5 N-4 N-3 N-2 N-1  N  N+1 N+2 N+3 N+4 N+5 N+6 N+7],:)=[];
% N = length(x);
%  K=randi([N+2 2*N],1);
%  p=floor((K-N)/2);
% pading=zeros(K-1,1);
% col_1=vertcat(x,pading);
% A=zeros(K+N-1,length(x));
% for ii=1:length(x)
%     col_ii= circshift(col_1,ii-1);
%     A(:,ii)=col_ii;
% end
% F=ones(1,2*N+2*p-1);
%  F=ones(1,length(x));
% F(N+p+2)=0;
% mat_F=diag(F);
% y=A*x;
% cost_func=y'*mat_F*y;
% Define optimization variables
% p=N;
p=floor(N/2-1);
A=real(A);
W=real(W);
cvx_begin

Unrecognized function or variable 'cvx_begin'.

variables y(N)  t 
% Define objective function
minimize t 
% Define constraints
subject to
(x'*y) == (x'*x)
for i =1:2*p-1
    
    if abs(i) >= N_L
        
        ((y')*(A(i,:)'))*A(i,:)*y <= t 
    else
        
        ((y')*(W(i,:)'))*W(i,:)*y <= beta(abs(i))    
    end
end   
%         for o = 1:2*N_L-1
%                 
%                ((y')*(W(o,:)'))*W(o,:)*y <= beta(abs(o))
%        end


%             for i =-p:p
%                  if abs(i) >= N_L
%                (( y')*(A(i+N+p,:))')*A(i+N+p,:)*y <=t
%                  end
%             end
%             for o = 1:2*N_L
%                (( y')*(A(o+N+p,:))')*A(o+N+p,:)*y <= beta(abs(o))
%             end
(y'*y) <= (alpha)*(x'*x);
cvx_end
%%
x_tcorr=abs(xcorr(x_t));
x_tcorr=x_tcorr/max(x_tcorr);
[val,indx]=findpeaks(x_tcorr);
sortval=sort(val,'descend');
SLL=pow2db((sortval(2)/sortval(1))^2)
mmf=abs(xcorr(x,y));
plot(20*log10(mmf/max(mmf)))
hold on 
plot(20*log10(x_tcorr))
x_tcorr1=abs(xcorr(y));
x_tcorr2=x_tcorr1/max(x_tcorr1);
%   plot(20*log10(x_tcorr2))
[val,indx]=findpeaks(x_tcorr2);
sortval1=sort(val,'descend');
SLL2=pow2db((sortval1(2)/sortval1(1))^2)

[Walter Roberson]

Requires http://cvxr.com/cvx/

[Walter Roberson]

minimize t

But nothing in the constraints involves t so the minimum is going to be at one of the infinities.

[Mohamed]

but the constraints already involves t

subject to

(x'*y) == (x'*x)

for i =1:2*p-1

if abs(i) >= N_L

((y')*(A(i,:)'))*A(i,:)*y <= t

else

((y')*(W(i,:)'))*W(i,:)*y <= beta(abs(i))

end

end

[Torsten]

Maybe abs(i) is always < N_L for your system ?