A paper written by ISE Grad Student Xiaolong Kuang in collaboration with Professor Luis F. Zuluaga, has been named one of the two winners of the 2019 Journal of Global Optimization Best Paper Award for their work entitled "Completely Positive and Completely Positive Semidefinite Tensor Relaxations For Polynomial Optimization". The Journal of Global Optimization is a journal Dealing with theoretical and computational aspects of seeking global optima and their application.
The Journal of Global Optimization Best Paper Award carries a $1,000 USD prize. This year the Best Paper Award Selection Committee included Leo Liberti, Ivana Ljubic, Ruth Misener, Jean-Philippe Richard.
The abstract for Xiaolong Kuang and Professor Luis F. Zuluaga's winning paper is as follows:
Completely positive (CP) tensors, which correspond to a generalization of CP matrices, allow to reformulate or approximate a general polynomial optimization problem (POP) with a conic optimization problem over the cone of CP tensors. Similarly, completely positive semidefinite (CPSD) tensors, which correspond to a generalization of positive semidefinite (PSD) matrices, can be used to approximate general POPs with a conic optimization problem over the cone of CPSD tensors. In this paper, we study CP and CPSD tensor relaxations for general POPs and compare them with the bounds obtained via a Lagrangian relaxation of the POPs. This shows that existing results in this direction for quadratic POPs extend to general POPs. Also, we provide some tractable approximation strategies for CP and CPSD tensor relaxations. These approximation strategies show that, with a similar computational effort, bounds obtained from them for general POPs can be tighter than bounds for these problems obtained by reformulating the POP as a quadratic POP, which subsequently can be approximated using CP and PSD matrices. To illustrate our results, we numerically compare the bounds obtained from these relaxation approaches on small scale fourth-order degree POPs.
The ISE department congratulates Xiaolong Kuang and Professor Luis F. Zuluaga for their excellent contribution to literature.