Operations Research Seminar: Erling Andersen

Joint INMA/CORE seminar

A primal-dual interior-point algorithm for non symmetric conic optimization

Erling Andersen, MOSEK

It is well known that primal-dual interior-point algorithms for linear optimization can easily be extended to the case of symmetric conic optimization, as shown by Nesterov and Todd (NT) in their 1997 paper about self-scaled barriers. Although many convex optimization problems can be expressed using symmetric cones then models involving for instance exponential functions do not belong to the class of symmetric conic optimization problems. Therefore, several authors have suggested generalizations of the NT primal-dual interior-point algorithm to handle nonsymmetric cones such as the exponential cone. Based on this work we will present a generalization of the NT algorithm to the case of nonsymmetric conic optimization. Although we have no polynomial complexity proof for the suggested algorithm then it performs extremely well in practice as will be documented with computational results. To summarize, this presentation should be interesting for users of convex optimization.