How to find parameters from logistic equation

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I have an function and assume that that is convex function. I want to use gradient decent to find parameters in that equation. Could you suggest to me the way to do it. Thanks. This is my function $$J=\int B(x) \times \left[\frac {1}{1+e^{-{ax+b}}}-L \right ]^2$$ where $L=\{-1;1\}$, B is Gaussian kernel that such that $\int B(x)=1$

How to find $a$,$b$ subject to $min_{a,b}J$

That mean I will compute $$\frac {\partial J}{\partial a}=0$$ $$\frac {\partial J}{\partial b}=0$$

Could you help me find two above equation?