=== ORFE Miscellaneous Talk Announcement ===

DATE:  Thursday, October 30, 2014

TIME:  2:00pm

LOCATION:   Sherrerd Hall, 101

SPEAKER:  Venkat Chandrasekaran, California Institute of Technology

TITLE:  Relative Entropy Relaxations for Signomial Optimization

ABSTRACT:  The relative entropy function plays a prominent role in a
variety of contexts in information theory and statistics. In this talk,
we discuss some of its beneficial computational properties that are a
consequence of its joint convexity with respect to both its arguments.
Signomial programs (SPs) are optimization problems specified in terms of
signomials, which are weighted sums of exponentials composed with linear
functionals of a decision variable. SPs are non-convex optimization
problems in general, and families of NP-hard problems can be reduced to
SPs. We describe a hierarchy of convex relaxations to obtain
successively tighter lower bounds of the optimal value of SPs. This
sequence of lower bounds is computed by solving increasingly
larger-sized relative entropy optimization problems, which are convex
programs specified in terms of linear and relative entropy functions.
Our approach relies crucially on the observation that the relative
entropy function provides a convex parametrization of certain sets of
globally nonnegative signomials with efficiently computable
nonnegativity certificates via the arithmetic-geometric-mean inequality.
By appealing to representation theorems from real algebraic geometry, we
show that our sequences of lower bounds converge to the global optima
for broad classes of SPs. Finally, we also demonstrate the effectiveness
of our methods via numerical experiments. (Joint work with Parikshit Shah)

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