Xin Liu

A Tight SDP Relaxation for the Cubic-Quartic Regularization Problem

Abstract This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem $$ \min _{s \in \mathbb {R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\frac{\beta }{6}\Vert s \Vert ^3+ \frac{\sigma }{4} \Vert s\Vert ^4, $$ min s ∈ R n f 0 + g T s + 1 2 s T...