Publication Date



Technical Report: UTEP-CS-20-32


In general, if we know the values a and b at which a continuous function has different signs -- and the function is given as a black box -- the fastest possible way to find the root x for which f(x) = 0 is by using bisection (also known as binary search). In some applications, however -- e.g., in finding the optimal dose of a medicine -- we sometimes cannot use this algorithm since, for avoid negative side effects, we can only try value which exceed the optimal dose by no more than some small value δ > 0. In this paper, we show how to modify bisection to get an optimal algorithm for search under such constraint.