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Title: Factorization of completely positive matrices using iterative projected gradient steps

Speaker: Radu Ioan Bot Affiliation: University of Vienna Zoom: Register through The Fields Institute

Abstract:

We aim to factorize a completely positive matrix by using an optimization approach which consists in the minimization of a nonconvex smooth function over a convex and compact set. To solve this problem we propose a projected gradient algorithm with parameters that take into account the effects of relaxation and inertia. Both projection and gradient steps are simple in the sense that they have explicit formulas and do not require inner loops. We show that the sequence of generated iterates

Title: Structured (In)Feasibility: Nonmonotone Operator Splitting in Nonlinear Spaces

Speaker: Russell Luke Affiliation: University of Goettingen Zoom: Register through The Fields Institute

Abstract:

The success of operator splitting techniques for convex optimization has led to an explosion of methods for solving large-scale and nonconvex optimization problems via convex relaxation. This success is at the cost of overlooking direct approaches to operator splitting that embrace some of the more inconvenient aspects of many model problems, namely nonconvexity, nonsmoothness, and infeasibility.