Fatma Kılınç-Karzan is awarded the Prize for Young Researchers for her paper, "On Minimal Valid Inequalities for Mixed Integer Conic Programs," Mathematics of Operations Research accepted for publication (2015), which studies disjunctive conic sets involving a general non-polyhedral cone. Within the context of mixed-integer conic programs, the paper addresses a number of fundamental questions, such as dominance relations among valid inequalities, introduces the notion of conic-minimality and establishes necessary and sufficient conditions, as well as practical tools, for testing whether a given inequality is conic-minimal or not.
Javad Lavaei and Somayeh Sojoudi are awarded the Prize for Young Researchers for their paper, "Exactness of Semidefinite Relaxations for Nonlinear Optimization Problems with Underlying Graph Structure," SIAM J. Optimization 24 (2014), pp. 1746-1778, which extends Lavaei's highly-cited recent work on the optimal power flow problem to address a broad class of nonlinear global optimization problems, including quadratic and polynomial optimization problems. Through the use of conic relaxations and elaborate graph theoretic techniques, the paper derives necessary and sufficient conditions for the exactness of certain relaxations for these problems. As a consequence, it is proved that relatively large classes of real and complex optimization problems over power networks are polynomial-time solvable due to the physics of power grids.
Nick Sahinidis (chair), Dan Bienstock, Sam Burer, Andrew Schaefer