[Ml-stat-talks] Fwd: [ORFE-Seminars] Seminar of Interest

Barbara Engelhardt bee at princeton.edu
Thu Feb 2 09:33:16 EST 2017

Talk of interest.

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* IAS - Computer Science/Discrete Mathematics Seminar II Topic: *Optimization
in dynamical systems

*Date & Time: *Tuesday February 7th, 2017, 10:30am - 12:30pm

In recent years, there has been a surge of exciting research activity at
the interface of optimization (in particular polynomial, semidefinite, and
sum of squares optimization) and the theory of dynamical systems. In this
talk, we focus on two problem classes on this boundary: In part (I), after
a brief review of nonnegative polynomials and Lyapunov functions, we
provide hardness results and semidefinite programming (SDP) based
relaxations for the problem of testing asymptotic stability of (i)
polynomial dynamics in continuous time, and (ii) switched linear dynamics
in discrete time. The latter problem is equivalent to that of computing the
joint spectral radius of a finite set of matrices. Based on connections to
standard concepts in automata theory, we provide a meta-theorem that
characterizes all SDPs which upper bound the joint spectral radius. We also
give approximation guarantees on the bound returned by many of these SDP
families. In part (II), we introduce a new class of optimization problems
which have constraints imposed by trajectories of a dynamical systems. As a
concrete example, we consider the problem of optimizing a linear function
over a subset of a polyhedron that never leaves it under the action of a
linear, or a switched linear, dynamical system. We show that under some
conditions, this problem can be solved in polynomial time by linear
programming, and under some other, approximated in polynomial time by
semidefinite programming. The talk is meant to be self-contained. Joint
work (in different subsets) with Oktay Gunluk, Raphael Jungers, Pablo
Parrilo, and Mardavij Roozbehani.

*Speaker: *Amir Ali Ahmadi

*Affiliation: *Princeton University

*Location:  *Institute for Advanced Studies
                     1 Einstein Drive
                     Princeton, NJ
                     Room S-101

Barbara E Engelhardt
Assistant Professor
Department of Computer Science
Center for Statistics and Machine Learning
Princeton University
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