Aims,background,,justification & scope of the use of gradient method in solving an unconstrained optimization.

Answer 1

that is a VERY broad question

main idea is, that if the goal f depends continually on parameters a, b, c, ...,

f = f(a,b,c,...)

and the gradient

(df/da, df/db, df/dc, ...)

is non-zero, then a higher value is found in the direction given by the gradient. Carfully adjusting the parameters in that direction may lead to finding a point with gradient zero, which then is local maximum.

The usefulness of this method depends greatly on the overall behavior of the function.