Strong convexity of sandwiched entropies and related optimization problems

Article Type

Research Article

Publication Title

Reviews in Mathematical Physics

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 n-coupling problem) for Gaussian measures.

DOI

10.1142/S0129055X18500149

Publication Date

10-1-2018

Comments

All Open Access, Green

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