Exploiting Constant Trace Property in Large-scale Polynomial Optimization

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with ball constraint can be reformulated as program involving matrix constant trace property (CTP). As result such relaxations solved efficiently by first-order methods exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. also extend this CTP-exploiting framework to large-scale POPs different sparsity structures. The efficiency and scalability our are illustrated on second-order for various randomly generated quadratically constrained quadratic programs.