Publication Date



Technical Report: UTEP-CS-20-56


It is known that, in general, the problem of computing the range of a given polynomial on given intervals is NP-hard. For some NP-hard optimization problems, the approximate version -- e.g., if we want to find the value differing from the maximum by no more than a factor of 2 -- becomes feasible. Thus, a natural question is: what if instead of computing the exact range, we want to compute the enclosure which is, e.g., no more than twice wider than the actual range? In this paper, we show that this approximate version is still NP-hard, whether we want it to be twice wider or k times wider, for any k.