Journal of Complexity ( IF 1.338 ) Pub Date : 2019-08-24 , DOI: 10.1016/j.jco.2019.101427 Leszek Plaskota; Paweł Siedlecki; Henryk Woźniakowski
Two classes of information have been mainly considered in Information-Based Complexity (IBC) for approximate solutions of continuous problems. The first class is and consists of all linear functionals, whereas the second class is and consists of only function evaluations. A different class of information has been studied in the context of phase retrieval, where it is assumed that only absolute values of linear functionals from are available. We denote this class and call it the absolute value information class. For we need to modify the algorithm error to compensate the missing phase in information values.
The purpose of this paper is to establish the powers of and in comparison to and for various IBC problems in the worst case setting. Our main result is that is roughly of the same power as for linear IBC problems. On the other hand, is usually too weak to solve linear problems.