We consider an infeasible predictor-corrector primal-dual path following interior point algorithm to solve semi-definite linear complementarity problems (SDLCPs). The well-known Nesterov-Todd (NT) search direction is used in the algorithm. We provide the best known polynomial complexity when the algorithm is used to solve SDLCPs, and also give two sufficient conditions for when local superlinear convergence of iterates generated by the algorithm occurs.
joint work with Spyridon Pougkakiotis, Jacek Gondzio
In this work we propose an ADMM based framework for solving large scale quadratic optimization problems. We focus on non-separable dense and huge-scale sparse problems for which the current interior point methods do not bring satisfactory performance in terms of run time or scalability. We show that by integrating first and second order methods we can achieve a significant boost in performance with a limited loss in solution quality.
Going over from the continuous (analytical) to the discrete (applied) setting one can use an "algebraic barrier" to get a family of (primal) "non-commutative" feasible-interior-point methods which are in particular useful for polynomial optimization (using sum-of-squares). I'm going to summarize the main ideas of my recent preprint arxiv:1812.10278 and show how an algebraic center can be used in different ways to find "good" minimization directions.