This paper studies a numerical optimization-based extremum seeking scheme for systems with unmodeled dynamics and unknown disturbances without using dither signals. The robust extremum seeking scheme is composed of a numerical gradient estimator, a numerical optimizer and an extended-state observer based state regulator. A conjugate gradient method is adopted to achieve extremum seeking. A nonlinear extended-state observer based state regulator is proposed to regulate the states. The robust extremum seeker is based on the numerical optimization based extremum seeking framework. Sufficient conditions are derived to ensure the convergence of the overall extremum seeking scheme. The ultimate convergence bound is quantified for a class of strongly convex functions. A numerical example is presented to verify the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.