Performance enhancements for a generic conic interior point algorithm

In recent work, we provide computational arguments for expanding the class of proper cones recognized by conic optimization solvers, to permit simpler, smaller, more natural formulations. We define an exotic cone as a which can implement small set tractable (i.e. fast, numerically stable, analytic) oracles logarithmically homogeneous self-concordant barrier or its dual cone. Our extensible, open source interior point solver, Hypatia, allows modeling and solving any problem over Cartesian product cones. this paper, introduce Hypatia's algorithm. algorithm is based on that Skajaa Ye [2015], generalize handling without primal oracles. With goal improving iteration count solve time in practice, propose sequence four enhancements stepping procedure [2015]: (1) loosening central path proximity condition, (2) adjusting directions using third order directional derivative oracle, (3) performing backtracking search curve, (4) combining prediction centering directions. 23 useful Hypatia. summarize complexity computing these cones, showing our new oracle not bottleneck, derive efficient stable implementations several generate diverse benchmark 379 problems from 37 different applied examples. testing shows each enhancement improves time. Altogether, reduce shifted geometric means 80% 70% respectively.