What I face: I would like to maximize the "energy" of variable x governed by a dynamical system equation dx/dt=g(x) at time T. The "energy" of x is defined as E(t)=x^2/2, since x is a function of time. x could be a vector or a scalar.
The optimisation problem is formulated as follows. I would like to find the best initial condition x_0 which will achieve the maximum energy at time T over all the other initial conditions.
The SGD method in the textbook is usually formulated as 
where \omega is the parameter to be optimised, X is some random variable and f is some function.
What I want to ask: it seems difficult to me to fit the optimisation problem I defined above in the formulation of the SGD. May I ask if you have any ideas?
