SESOP-TN is a method for very large scale unconstrained optimization of smooth functions. It combines ideas of Sequential Subspace Optimization (SESOP) [Narkiss-Zibulevsky-2005] with those of the Truncated Newton (TN) method . Replacing TN line search with subspace optimization, we allow Conjugate Gradient (CG) iterations to stay matched through consequent TN steps. This resolves the problem … Read more
In this paper we derive the efficiency estimates of the regularized Newton’s method as applied to constrained convex minimization problems and to variational inequalities. We study a one-step Newton’s method and its multistep accelerated version, which converges on smooth convex problems as $O({1 \over k^3})$, where $k$ is the iteration counter. We derive also the … Read more
We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s Method, the relationship of the majorant function and the non-linear operator under consideration. This approach enable us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate … Read more
We study a relative optimization framework for quasi-maximum likelihood blind source separation and relative Newton method as its particular instance. The structure of the Hessian allows its fast approximate inversion. In the second part we present Smoothing Method of Multipliers (SMOM) for minimization of sum of pairwise maxima of smooth functions, in particular sum of … Read more
In this paper, we survey the most recent methods that have been developed for the solution of semidefinite programs. We first concentrate on the methods that have been primarily motivated by the interior point (IP) algorithms for linear programming, putting special emphasis in the class of primal-dual path-following algorithms. We also survey methods that have … Read more