Alfonso: Matlab Package for Nonsymmetric Conic Optimization

We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method Skajaa and Ye. It enables any cone as long logarithmically homogeneous self-concordant barrier available or its dual. This includes many cones, example, hyperbolicity cones their duals (such sum-of-squares cones), semidefinite second-order representable power exponential cone. Besides enabling solution that cannot be cast symmetric cone, algorithms also offer performance advantages whose programming representation requires large number auxiliary variables has special structure can exploited in computation. worst-case iteration complexity alfonso best known optimization: [Formula: see text] iterations to reach ?-optimal solution, where ? parameter function used optimization. Alfonso interfaced with (supplied by user) computes Hessian A simplified interface optimize direct product which already been built into software. easily extended include new Both interfaces are illustrated linear programs. oracle efficiency demonstrated using optimal design experiments problem tailored computation greatly decreases time compared state-of-the-art, off-the-shelf Summary Contribution: paper describes particularly important feature this software that, unlike other software, it suitable dual, not limiting user small specific Nonsymmetric such barriers include, Thus, scope far larger than most current does come at price efficiency, our algorithm matches successful interior-point methods via example code significantly outperforms Mosek 9 SCS 2.