joint work with Levent Tuncel
In this talk, we introduce the Domain-Driven form for convex optimization problems and show how general it is by several examples. We have designed infeasible-start primal-dual interior-point algorithms for the Domain-Driven form, which accepts both conic and non-conic constraints. Our algorithms enjoy many advantages of primal-dual interior-point techniques available for conic formulations, such as the current best complexity bounds. At the end, we introduce our software package DDS created based on our results for many classes of convex optimization problems.
joint work with Etienne de Klerk
We analyze the simulated annealing algorithm by Kalai and Vempala [Math of OR 31.2 (2006): 253-266] using the temperature schedule put forward by Abernethy and Hazan [arXiv 1507.02528v2, 2015]. This algorithm only assumes a membership oracle of the feasible set, and returns a solution in polynomial time which is near-optimal with high probability. Moreover, we propose a number of modifications to improve the practical performance of this method. Numerical examples show the method has an application to convex problems where no other method is readily available, such as copositive programming.
joint work with Sercan Yildiz
Many optimization problems can be conveniently written as conic programs over non-symmetric cones; however, these problems are lacking the solver support that symmetric conic optimization problems have. We propose alfonso, a highly general Matlab-based interior point solver for non-symmetric conic optimization. Alfonso can solve optimization problems over a cone as long as the user can supply the gradient and Hessian of a logarithmically homogeneous self-concordant barrier for either the cone or its dual. We demonstrate its efficiency using non-symmetric cones arising in polynomial programming