Solving natural conic formulations with Hypatia.jl

Understand

Many convex optimization problems can be represented through conic extended formulations with auxiliary variables and constraints using only the small number of standard cones recognized by advanced conic solvers such as MOSEK 9.

• Such extended formulations are often significantly larger and more complex than equivalent conic natural formulations, which can use a much broader class of exotic cones.
• We define an exotic cone as a proper cone for which we can implement tractable logarithmically homogeneous self-concordant barrier oracles for either the cone or its dual cone.
• In this paper we introduce Hypatia, a highly-configurable open-source conic primal-dual interior point solver with a generic interface for exotic cones.