Alternative SDP and SOCP Approximations for Polynomial Optimization

Understand

In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP).

• However, due to the computational challenge of solving SDPs, it becomes difficult to use SDP hierarchies for large-scale problems.
• To address this, hierarchies of second-order cone programming (SOCP) relaxations resulting from a restriction of the SOS polynomial condition have been recently proposed to approximate POPs.
• Here, we consider alternative ways to use this SOCP restrictions of the SOS condition.