Sanjay Mehrotra (left), Jiawang Nie, and Andrzej Ruszczyński.
The 2014 recipient of the Prize for Young Researchers of the INFORMS Optimization Society is Jiawang Nie, for the his paper "Optimality conditions and finite convergence of Lasserre's hierarchy," Mathematical Programming, Ser. A (2014) 146:97-121, DOI: 10.1007/s10107-013-0680-x.
In this paper, Jiawang Nie proves that Lasserre's hierarchy of semidefinite relaxations for global polynomial optimization has finite convergence, when the usual standard constraint qualification, strict complementarity, and second order sufficiency conditions of nonlinear programming hold at all global minimizers. Moreover, he shows that these sufficient conditions hold generically at any (local or global) minimizer, whenever a fixed degree bound on the defining polynomials exist.
Prior to this work, the existing theory could only establish the convergence of this family of relaxations in the limit. No proof of finite convergence had been previously found in spite of the significant numerical evidence for finite convergence that had been collected over a decade or so. Jiawang's contribution will stand out for many years to come and will likely shape further research in an important and very active area of polynomial optimization.
Jiawang Nie was invited to give a short talk (about 15 minutes) at the INFORMS Annual Meeting. Here is the link to the recording of his talk.
Andrzej Ruszczyński (chair), Katya Scheinberg, Javier Peña, Jean-Philippe Richard