Dep. of Automatic Control and Systems Engineering
University Politehnica Bucharest
In this talk we analyze dual first order methods based on (inexact) gradient information and averaging that generate approximate primal solutions for smooth convex problems. The complicating constraints are moved into the cost using the Lagrange multipliers. Then, the dual problem is solved by (inexact) first order methods for which we prove sublinear or even linear rate of convergence. For the approximate primal solutions we consider both cases: an average primal sequence and the last iterate sequence. We provide a unified rate analysis and estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Applications and numerical tests on embedded MPC are also provided.
Ion Necoara received the B.Sc. degree in mathematics and the M.Sc. degree in optimization and statistics from the University of Bucharest, in 2000 and 2002. After graduating he worked as a Ph.D. student at the Delft Center for Systems and Control, Delft University of Technology, the Netherlands. For the period 2006–2009, he completed a Postdoctoral Fellowship at the Katholieke Universiteit Leuven, Belgium. Since 2009 he is a staff member of the Faculty of Automatic Control and Computers, University Politehnica Bucharest, where he is now an Associate Professor of Numerical Methods and Optimization. His main research interests cover various topics in developing new optimization algorithms with a focus on structure exploiting and applying optimization techniques for developing new advanced controller design algorithms for complex systems.
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