Title
Introducing Loraine – a Solver for Low-Rank Semidefinite Optimization
Abstract
The aim of this talk is to introduce a new code for the solution of large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions and/or low-rank data. We propose to use a preconditioned conjugate gradient method within an interior-point SDP algorithm and an efficient preconditioner fully utilizing the low-rank information. The efficiency will be demonstrated by numerical experiments using, among others, Lasserre relaxations of the MAXCUT problems and the sensor network localization problems. The code is available in Matlab and Julia, admits input in several standard SDP input formats and can be used not only for low-rank problems but for any linear SDP.
Bio
Professor Michal Kočvara’s research interests include nonlinear and semidefinite optimisation, optimisation of elastic structures, and optimisation with equilibrium constraints. Before joining the academic sphere, he worked for several years in the industry. He is particularly skilled to create a bridge between academic research and practical needs of the industry.
Before joining the University of Birmingham in January 2007, he was with the Academy of Sciences of the Czech Republic and, simultaneously, working on research projects at the Universities in Bayreuth and Erlangen, Germany.
His recent work has been supported by Horizon 2020 (ITN) and EPSRC (Bridging-the-Gap), and involves several academic and industrial partners across Europe. Michal is a (co-)author of a monograph and over 50 journal articles on various aspects of mathematical optimisation and optimisation of mechanical structures. He developed or co-developed several computer programs for non-linear optimisation and optimisation of elastic structures, some of them routinely used in academia and industry. He was a long-term visitor at the Institute of Mathematics and its Applications, University of Minnesota (2003), the Technical University of Denmark (2007) and the Institute for Pure and Applied Mathematics, UCLA (2010).