Seminar - Cunlu Zhou, University of Notre Dame
Quantum (von Neumann) entropy optimization problems constitute an important class of quantum relative entropy optimization and have applications in various areas including quantum state tomography, statistical physics and machine learning. The optimization involves a nonlinear convex objective function $Tr(XlnX)$ and equality constraints on positive definite matrix $X$. In this talk I will present a long-step interior-point algorithm for the quantum entropy optimization (joint work with my co-advisor).Our interior-point method takes a direct approach to the optimization problem and can exploit the full structural properties of a concrete problem. Numerical results show that our algorithm has the best performance compared to other available options. In addition, complexity estimates similar to a linear objective function are established. I will explain both the theoretical aspects of the algorithm and its numerical implementations. In the end I will discuss some recent work in extending our algorithm to the relative entropy optimization.