if I add this constrain in my code, the result of cvx will be inf. But if i remove it, the cvx can give a result and the result satisfy this constrain. In the contation tk is convex the T_H and T_F are real affine. t_c is constant.
Can you provide a reproducible problem (hopefully, simplest and smallest possible exhibiting the behavior) , complete with all input data? Or at least all solver and CVX output, including your claimed constraint satisfaction? Have you tried other solver(s)?
If this is not a bug, perhaps thee problem has bad scaling. What are the smallest and largest magnitudes of non-zero numbers in the input data? Very small or large magnitudes might cause “erroneous” behavior of the solver on such matters as feasibility deterrmination.