Formulating Steepest Descent

Suppose that G is a 2D function RxR ---> R

function F is defined as follows:
F(x,y ,r ) = sum of all Gij's residing inside the circle with
radius r; centered at <x,y>.

given an initial state x0,y0,r0 , I want to minimize F using the
steepest descent method.


I think that the problem must be formulated as a double integral in
the polar coordinates but I cannot realize and implement it .

.

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