Title: Algorithms for Variational Inequalities and Solvers for Quadratic Programming Speaker: Aswin Kannan, Penn. State University Time: 3pm, 6/12/2013 (Friday) Venue: LCC 11, Lecture Hall Complex Abstract: This talk will focus on three different classes of problems arising in generic optimization settings. In the first part of the talk, we consider a class of monotone variational inequality problems. Two practically implementable regularization schemes, namely the Iterative Tikhonov and Proximal Point methods (ITR and IPP), are developed as extensions to standard Tikhonov and proximal point schemes. In contrast to standard schemes that solve a sequence of variational problems, the presented schemes require precisely one gradient or projection step at every iteration by suitably updating the corresponding regularization/centering parameters. Distributed generalizations for coping with multi-agent settings are also provided. A networked nonlinear Nash Cournot game is presented as a case study. Secondly, the stochastic generalization of such a problem is considered wherein the mapping is pseudomonotone is studied. An extragradient variant of stochastic approximation is proposed and under mild assumptions the almost-sure convergence of the resulting iterates is proved. Under slightly stronger assumptions, a rate of convergence analysis is provided. Some fractional convex problems are chosen as instances to study the performance of the proposed schemes. Finally, sparse convex quadratic optimization problems that present a relatively smaller interior from the standpoint of the constraints are considered. Some classic applications include response surface modeling, statistical learning and noisy derivative free optimization. Based on the problem structure, an efficient algorithm is presented. The associated solver implementation (NoQS) is seen to outperform generic quadratic programming solvers. About the speaker: Aswin Kannan is currently a doctoral student at Penn State (2012-). Prior to this, he worked at Argonne National Labs from 2010 to 2012. His research interests are in optimization and scientific computing. He also holds a Masters degree from University of Illinois at Urbana Champaign (2010) and a Bachelors degree from College of Engineering Guindy, Chennai, India(2008).
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