# Is this Problem Convex? if not, what should I change to make it convex

N=4;
A1=[eye(N-1) zeros(N-1,1)];
B=[zeros(1,N); A1];
Es=10;
c1=9.26*10^(-4);
c2=2250;
amax=20;
vmin=1;
vmax=10;
del=0.01;
var_del=1;
gamma=0.02;
q0=[0 0];
qf=[20 50];
v0=[1 1];
vf=[10 10];
Rt=10;
H=50;
B=50;
g=10;
cvx_begin
variables q1(N) q2(N) v1(N) v2(N) a1(N) a2(N) Eb;
minimize Eb;
subject to

``````  V=[v1(N) v2(N)];
Q=[q1(N) q2(N)];
A=[a1(N) a2(N)];
x=norm(V);
B*q1 == q1+del*v1+(0.5*del^2)*a1;
B*q1 == q1+del*v1+(0.5*del^2)*a1;
B*q2 == q2+del*v2+(0.5*del^2)*a2;
B*v1 == v1 +del*a1;
B*v2 == v2 +del*a2;
q1(1)==q0(1);
q2(1)==q0(2);
q1(N)==qf(1);
q2(N)==qf(2);
v1(1)==v0(1);
v2(1)==v0(2);
v1(N)==vf(1);
v2(N)==vf(2);
v1.^2+v2.^2  <= (vmax^2)*ones(N,1);
a1.^2+a2.^2  <= (amax^2)*ones(N,1);
c1*(pow_pos(norm(V),3))+(c2*inv_pos(-norm(V)))+((1+norm(A))./g^2+var_del/del)<=0;

c1*(pow_pos(norm(V),3))+c2*(inv_pos(-norm(V))*(1+norm(A)))./g^2+var_del/del)'*ones(N,1)<=(Es+Eb);
(B*log2(1+gamma/(H^2+pow_p(q1,2)+pow_p(q2,2))))'*ones(N,1)<=Rt;
``````

end_cvx

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