A Semidefinite Relaxation Scheme for Multivariate Quartic Polynomial Optimization with Quadratic Constraints

We present a general semidefinite relaxation scheme for general n-variate quartic polynomial optimization under homogeneous quadratic constraints. Unlike the existing sum-of-squares (SOS) approach which relaxes the quartic optimization problems to a sequence of (typically large) linear semidefinite programs (SDP), our relaxation scheme leads to a (possibly nonconvex) quadratic optimization problem with linear constraints over the semidefinite matrix cone in Rn

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Zhi-Quan Luo, Shuzhong Zhang
• Keywords: Quadratic Constraint, Quartic Optimization Problem, Quartic Polynomial Optimization, SIAMJO 2010