[talks] ORFE Miscellaneous Talk: Venkat Chandrasekaran, Thursday, Oct. 30th at 2:00pm, Sherrerd Hall, 101

[Nicole E. Wagenblast]

=== 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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