Conventional radars have made extensive use of the linear frequency modulated (LFM) signals. Nevertheless, its radar detectability is negatively impacted by its high sidelobe level (SLL). Modern radars use nonlinear frequency modulated (NLFM) signals to overcome the masking problem by obtaining suppressed sidelobes of radar matching filter output while preserving the mainlobe level and resolution. In this paper, NLFM signals are optimized to get very low SLL while maintaining the mainlobe width (MLW) and hence improving range resolution and radar detection capabilities. An optimization framework will be introduced depending mainly on feasible direction methods which move towards the optimal solution iteratively within the feasible region to optimize the proposed NLFM signal that is generated by an instantaneous frequency function described by tan function. This framework relies on two nonlinear optimization techniques that are Zoutendijk's method of feasible directions (ZMFD) and Rosen's gradient projection method (RGPM). These methods solve the nonlinear optimization issue by advancing in the feasible search direction from a feasible point to an enhanced feasible one. Simulation results of the autocorrelation function (ACF) of the optimized NLFM signal reveal its superiority in suppressing SLL compared to LFM signal and preserving MLW of the radar signal. The detailed mathematical description of these two algorithms is also included in this work. Furthermore, two metrics are also calculated to ensure the quality of the resulted signals which are the impulse response width (IRW) and integrated sidelobe ratio (ISLR). Finally, all these results are tabulated to compare the two optimization techniques and the radar designers should choose the best technique depending on the radar system application.