Strong convexity of sandwiched entropies and related optimization problems

Abstract

We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrized 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 [Formula: see text]-coupling problem) for Gaussian measures.