Except the fifth constraint all other are linear constraints and I had no problem to write MATLAB code for these constraints. Since, fifth constraint is not in DCP form, I transform the fifth constraint as follows (after reading some posts in this forum):

z-2.5610^(-8)t2+10^(-19)x<=0.002;
{b1,s,t1}== rotated_lorentz(1)
{s,x,b1l}== rotated_lorentz(1)
{b2log(2)/(510^6),t2,z/(2.5610^(-8))}==exponential(1);
along with the above, also declared s, x, t1, t2, b1, b2>=0

It seems that the transformation of the fifth constraint is incorrect, since the solution I am getting using the above code is: V=t1=0.0216, t2=0.0016, b1=31.67, b2=1.9910^5. However, I know about a solution: V=0.0198, t1=0.0189, t2=0.0017, b1=1.8810^4, b2=1.81*10^5 which is a feasible solution and better than what I am getting from my code. Please let me know if the above transformation is correct?

I haven’t checked the correctness of your code. But the atrocious numerical scaling means that numerical results returned by the solver and CVX can’t be trusted. Numbers such as 1e6, 1e7, 1e-8, 1e-19 are horrible. Please read some of the pots talking about scaling.

Being a new to CVX, I am worried if the fifth constraint is correct? If you can kindly have a look on the DCP transformation of the fifth constrain (mainly concerned about the second term of the fifth constraint), that will be very helpful. I read some posts by you and @Michal_Adamaszek to prepare this code.

As per your suggestion, I will try to scale the problem.