The result of CVX solver is not the best point

supposing the variable to optimize is V, I did a Taylor expansion to make the problem convex.

if i do the Taylor expansion at V_0, obviously V_0 is a feasible resolution to my problem. But sometimes, after cvx, the V_{new} I got caused a worse result than V_0.

Could this be due to accuracy errors, or does it mean that my code has something wrongs?