Extremum seeking control (ESC) schemes based on numerical optimization are proposed in this paper. The extremum seeking problem is treated as an optimization with dynamic system constraints. The numerical optimization-based extremum seeking control scheme is first applied to lineat time-invariant (LTI) systems, then it is extended to a class of feedback linearizable systems. The convergence of the ESC scheme is guaranteed by the numerical optimization algorithm and state regulation. The robustness of line search methods and trust region methods is studied, which provides further flexibility for the design of robust extremum seeking controller. Simulation study of antilock braking systems (ABS) design via extremum seeking control is addressed.