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SUMMARY:Vortrag von Prof. Bahman Gharesifard
DESCRIPTION:Prof. Bahman Gharesifard \n Control Group Department of Mathematics and Statistics\nQueenÂ´s University,\nOntario, Canada \nTuesday 2016-06-28 16:00\n IST-Seminar-Room V9.22 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen \nAbstract \nIn the first part of this talk, we study the asymptotic convergence properties of the\nsaddle-point dynamics associated to continuously differentiable functions of two vector variables\nthat have (possibly a continuum of) min-max saddle points. We identify a suite of complementary\nconditions under which the set of saddle points is asymptotically stable under the saddle-point\ndynamics.\nIn the second part of the talk, we demonstrate the implications of these convergence result in\ndesigning continuous-time distributed convex optimization algorithm. We also demonstrate how such\ncontinuous-time dynamical systems can be formulated as the trajectories of a distributed control\nsystems, where the control input to the dynamics of each agent relies on an observer that estimates\nthe average state. Using this observation, and by incorporating a continuous-time version of the\nso-called push-sum algorithm, we relax the graph theoretic conditions under which the first\ncomponent of the trajectories of this modified class of saddle-point dynamical systems for\ndistributed optimization are asymptotically convergent to the set of optimizers. In particular, we\nprove that strong connectivity is sufficient under this modified dynamics, relaxing the commonly\nused weight-balanced assumption. As a by product, we also show that the saddle-point distributed\noptimization dynamics can be extended to time-varying weight-balanced graphs which satisfy a\npersistency condition on the min-cut of the sequence of Laplacian matrices.\n \nBiographical Information\n \nBahman Gharesifard is an Assistant Professor with the Department of Mathematics and Statistics,\nQueen's University, Canada. Prior to joining Queen's, he was a Postdoctoral Research Associate with\nthe Coordinated Science Laboratory (CSL) at the University of Illinois, Urbana-Champaign\n(2012-2013) and Postdoctoral Researcher at the Cymer Center for Controls and Dynamics at the\nUniversity of California in San Diego (2009-2012). He received a PhD degree in Mathematics from\nQueen's University, Canada, in 2009. His research interests include systems and controls,\ndistributed optimization, social and economic networks, game theory, geometric control and\nmechanics, and Riemannian geometry.\n\n
DTSTART;VALUE=DATE:20160628
URL;VALUE=URI:https://www.ist.uni-stuttgart.de/de/veranstaltungen/Vortrag-von-Prof.-Bahman-Gharesifard/
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