Strong convexity of sandwiched entropies and related optimization problems

Author:

Bhatia Rajendra1,Jain Tanvi2,Lim Yongdo3

Affiliation:

1. Ashoka University, Sonepat, Haryana, 131029, India

2. Indian Statistical Institute, New Delhi 110016, India

3. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

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.

Funder

National Research Foundation of Korea

J. C. Bose National Fellowship

SERB Women Excellence Award

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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