What is abs_h1_optt and why should it show any improvement?
You have implemented the bisection method for quasi-convex optimization described in section 4,2,5 of https://web.stanford.edu/boyd/cvxbook/, modified to do maximization instead of minimization. This method is to find the optimal (maximum) value of the objective Q. So whatever abs_h1_optt is, why should it show improvement?