<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: arial,helvetica,sans-serif; font-size: 12pt; color: #000000'><br><div style="color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt;">=== ORFE Miscellaneous Talk Announcement ===<br><br>DATE: Thursday, October 30, 2014<br><br>TIME: 2:00pm<br><br>LOCATION: Sherrerd Hall, 101<br><br>SPEAKER: Venkat Chandrasekaran, California Institute of Technology<br><br>TITLE: Relative Entropy Relaxations for Signomial Optimization<br><br>ABSTRACT: The relative entropy function plays a prominent role in a <br>variety of contexts in information theory and statistics. In this talk, <br>we discuss some of its beneficial computational properties that are a <br>consequence of its joint convexity with respect to both its arguments. <br>Signomial programs (SPs) are optimization problems specified in terms of <br>signomials, which are weighted sums of exponentials composed with linear <br>functionals of a decision variable. SPs are non-convex optimization <br>problems in general, and families of NP-hard problems can be reduced to <br>SPs. We describe a hierarchy of convex relaxations to obtain <br>successively tighter lower bounds of the optimal value of SPs. This <br>sequence of lower bounds is computed by solving increasingly <br>larger-sized relative entropy optimization problems, which are convex <br>programs specified in terms of linear and relative entropy functions. <br>Our approach relies crucially on the observation that the relative <br>entropy function provides a convex parametrization of certain sets of <br>globally nonnegative signomials with efficiently computable <br>nonnegativity certificates via the arithmetic-geometric-mean inequality. <br>By appealing to representation theorems from real algebraic geometry, we <br>show that our sequences of lower bounds converge to the global optima <br>for broad classes of SPs. Finally, we also demonstrate the effectiveness <br>of our methods via numerical experiments. (Joint work with Parikshit Shah)<br><br>**********************************************************<br><br></div><br></div></body></html>