[Ml-stat-talks] Fwd: [ORFE-Seminars] TODAY: PACM Colloquium: SEPT 25/Amir Ali Ahmadi

Barbara Engelhardt bee at princeton.edu
Mon Sep 25 09:06:06 EDT 2017


Talk of interest today.

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The next PACM Colloquium will be given by Amir Ali Ahmadi, Princeton
University


Title and abstract are below.


=================
DATE/LOCATION: Monday, Sept 25, 2017, 4:00 – 5:00 PM / 214 Fine Hall

SPEAKER: Amir Ali Ahmadi, Princeton University

TITLE:  Polynomial Optimization and Dynamical Systems



ABSTRACT:



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 of our current research directions that are at this
interface. In part (i), we propose more scalable alternatives to sum of
squares optimization and show how they impact verification problems in
control and robotics. Our new algorithms do not rely on semidefinite
programming, but instead use linear programming, or second-order cone
programming, or are altogether free of optimization. In particular, we
present the first Positivstellensatz that certifies infeasibility of a set
of polynomial inequalities simply by multiplying certain fixed polynomials
together and checking nonnegativity of the coefficients of the resulting
product.



In part (ii), we introduce a new class of optimization problems whose
constraints are imposed by trajectories of a dynamical system. As a
concrete example, we consider the problem of optimizing a linear function
over the set of initial conditions that forever remain inside a given
polyhedron under the action of a linear, or a switched linear, dynamical
system. We present a hierarchy of linear and semidefinite programs that
respectively lower and upper bound the optimal value of such problems to
arbitrary accuracy.

=================



Gina M. Holland

Princeton University

The Program in Applied and Computational Mathematics

205A Fine Hall

609-258-3703 <(609)%20258-3703> – phone

609-258-1735 <(609)%20258-1735> – fax

gholland at princeton.edu

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-- 
Barbara E Engelhardt
Assistant Professor
Department of Computer Science
Center for Statistics and Machine Learning
Princeton University
http://www.cs.princeton.edu/~bee
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