Computing real signal with minimum absolute values from even magnitude spectrum
Turns out this problem is known as crest factor minimization. I'm using an algorithm by Yang et al. (Phyiol. Meas. 36, 2015). Crest factor minimization algorithms typically are not proven to work on all possible magnitude spectra and only rarely proven to work on magnitude spectra with certain characteristics. Also, some iterative algorithms like Yang et al.'s have been shown in later publications to get stuck at a local minimum, not the global minimum. However, Yang et al.'s algorithm is satisfactory for the magnitude spectra I've tried so far.