Nonlinear Programming (NLP) is for optimization of nonlinear cost functions. In applications of NLP for real-time optimization, however, the estimation of the gradient of the cost function remains as a challenge. On the other hand, the Extremum-Seeking Control (ESC) optimizes the cost function in real-time, but it involves a complicated design of filters in multi-dimensional cases. In this paper, a new method that optimizes an arbitrary multi-variable cost function in real-time is proposed. In the proposed method, the variables are updated as in NLP while the gradient of the cost function is continuously estimated by the amplitude modulation as in ESC. The proposed method does not require design of any complicated filters. The performance is verified by simulations on time-varying and noisy cost functions as well as automatic controller tuning applications.

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