Algorithm to find the minimum value point of a function -

i find lowest value of function least number of trials. function f(x) must have point minimum value. given input x, can calculate f(x), not other direction. don't have explicit expression of function, blackbox.

i find input x such minimizes f(x), least number of trials (one trial when choose specific x, , plug in output). there algorithms achieve that?

the result doesn't need absolute minimum, since derived real problem. should less of values.

if function constrained convex, there better way achieve that?

thanks!

assuming function convex , derivative of f(x) exist points => there 1 minima. reason stressing derivative constrain in case when function looks 2 convex functions 1 next @ point of intersection derivative doesn't exist, function still convex , there 2 local minima.

the derivative have opposite signs left , right of minima (the slope changes directions) can see visualization of here. having in mind can simple binary search on domain find point k satisfies f'(k-e) * f'(k+e) < 0 smaller pick e, better precision of result. when doing search let [a,b] interval , k=(a+b)/2 select left if f'(k)*f'(a) < 0 , right otherwise.

having f(x), f'(x) = (f(x+e)-f(x))/e, again smaller pick e, better precision of derivative.