Strong convexity of sandwiched entropies and related optimization problems

被引：18

作者：

Bhatia, Rajendra ^{[1
]}

Jain, Tanvi ^{[2
]}

Lim, Yongdo ^{[3
]}

机构：

[1] Ashoka Univ, Sonepat 131029, Haryana, India

[2] Indian Stat Inst, New Delhi 110016, India

[3] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

来源：

REVIEWS IN MATHEMATICAL PHYSICS | 2018年 / 30卷 / 09期

基金：

新加坡国家研究基金会;

关键词：

Positive definite matrix; multimarginal optimal transport; fidelity; sand-wiched quasi-relative entropy; strong convexity; gradient projection algorithm; TRANSITION-PROBABILITY; DISTANCE; GEOMETRY;

D O I：

10.1142/S0129055X18500149

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：18

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