A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are second order cone programs (SOCP), semidefinite problems (SDP), and copositive problems. We survey recent progress made in this area. In particular, we highlight the connections between nonconvex quadratic problems, binary quadratic problems, and copositive optimization. We review how tight bounds can be obtained by relaxing the copositivity constraint to semidefinitness, and we discuss the effect that different modelling techniques have on the quality of the bounds.
Preprent, submitted (2021)