Strong Convexity of Sandwiched Entropies and Related Optimization Problems

Yongdo Lim

Department of Mathematics

Sungkyunkwan University

ylim@skku.edu

    We present several theorems on strict and strong convexity for sandwiched quasi-relative entropy (a parametrised version of the classical fidelity). These are crucial for establishing global linear convergence of the gradient projection algorithm for optimization problems for these functions. The case of the classical fidelity is of special interest for the multimarginal optimal transport problem (the `n`-coupling problem) for Gaussian measures. This is joint work with Rajendra Bhatia and Tanvi Jain.