Towards the optimal construction of a loss function without spurious local minima for solving quadratic equations

Zhenzhen Li, Jian-Feng Cai, Ke Wei

The problem of finding a vector $x$ which obeys a set of quadratic equations $|a_k^{\top }x{|}^2=y_k$, $k=1,\cdots ,m$, plays an important role in many applications. In this paper we co…