  Quasi-Newton techniques approximate the Newton step by estimating the Hessian
using the so-called secant equations. Some of these methods compute the Hessian
using several secant equations but produce non-symmetric updates. Other
quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more
than one secant equation. We propose a new type of quasi-Newton symmetric
update using several secant equations in a least-squares sense. Our approach
generalizes and unifies the design of quasi-Newton updates and satisfies
provable robustness guarantees.
