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|
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
converges to a critical point and provide the rate of convergence in terms of the \L ojasiewicz exponent of a regularization of the objective function. Numerical experiments demonstrate the efficiency of the proposed method, in particular in comparison to other factorization algorithms, and emphasize the role of the relaxation and inertial parameters. The talk is based on a joint work with D.-K. Nguyen.
Bio: Radu Ioan Bot is Professor for Applied Mathematics with Emphasis on Optimization at the Faculty of Mathematics of the University of Vienna and Member of the Research Platform "Data Science@Uni Vienna''. Currently, he is the Dean of the Faculty of Mathematics and the Speaker of the Vienna Graduate Doctoral School on Computational Optimization.
Radu Ioan Bot's research interests include nonsmooth analysis, numerical algorithms for convex and nonconvex optimization and minimax problems, monotone operator theory, dynamical systems, and optimization methods for data science. His research has been funded by the Austrian Science Fund, the German Research Foundation, the Romanian National Research Council, the Australian Research Council, and by industrial partners. He is (co-) author of the books "Duality in Vector Optimization" and "Conjugate Duality in Convex Optimization" published by Springer.
Radu Ioan Bot is member of the Editorial Board of the journals Applied Mathematics and Optimization, Computational Optimization and Applications, Optimization Methods and Software, Optimization Letters, Journal of Optimization Theory and Applications, and SIAM Journal on Optimization.