High-Dimensional Optimization and Probability: With a View Towards Data Science

This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces.

The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas.

Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

​Ashkan Nikeghbali is currently Chair of the department of quantitative finance at the University of Zürich. His fields of research include finance mathematics, number theory, random matrices, and stochastic processes. Since 2016 Prof. Nikeghbali has been a member of the Scientific Advisory Board of swissQuant and a member of the Advisory Board of EVMTech.
Panos M. Pardalos serves as distinguished professor of industrial and systems engineering at the University of Florida. Additionally, he is the Paul and Heidi Brown Preeminent Professor of industrial and systems engineering. Professor Pardalos is also an affiliated faculty member of the computer and information science department, the Hellenic Studies Center, and the biomedical engineering program. Additionally, he serves as the director of the Center for Applied Optimization. Professor Pardalos is a world leading expert in global and combinatorial optimization. His recent research interests include network design problems, optimization in telecommunications, ecommerce, data mining, biomedical applications, and massive computing. Panos Pardalos is a prolific author who lectures all over the world. He is the recipient of a multitude of fellowships and awards, the most recent of which is the Humboldt Research Award (2018).

Andrei Raigorodskii is a Federal Professor of Mathematics at the Moscow Institute of Physics and Technology (MIPT) where he is the Director of the Phystech-School of Applied Mathematics and Computer Science, the Head of the Discrete Mathematics Department, the Head of the Laboratory of Advanced Combinatorics and Network Applications, as well as the Head of the Laboratory of Applied Research MIPT-Sberbank. He is also the Head of the Caucasus Mathematical Center. He lectures at MIPT, MSU, HSE and has published about 200 papers and 20 books. He is the Editor-in-Chief of the Moscow Journal of Combinatorics and Number Theory. In 2011, he was awarded the 2011 Russian President's Prize in Science and Innovation for young scientists.

Michael Th. Rassias is a Research Fellow at the University of Zürich and a visiting researcher at the Institute for Advanced Study, Princeton. While conducting postdoctoral research at the Department of Mathematics of Princeton University in 2014-2015, he prepared with John F. Nash, Jr. the volume "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. In 2014 he was awarded with the Notara Prize by the Academy of Athens. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach's conjecture, the distribution of prime numbers, approximation theory, functional equations and analytic inequalities.

Ashkan Nikeghbali目前是蘇黎世大學量化金融系的主任。他的研究領域包括金融數學、數論、隨機矩陣和隨機過程。自2016年以來，Nikeghbali教授一直是swissQuant科學顧問委員會和EVMTech顧問委員會的成員。

Panos M. Pardalos是佛羅里達大學工業和系統工程系的傑出教授。此外，他還是佛羅里達大學工業和系統工程系的Paul和Heidi Brown卓越教授。Pardalos教授還是計算機和信息科學系、希臘研究中心和生物醫學工程項目的聯合教職成員。此外，他還擔任應用優化中心的主任。Pardalos教授是全球和組合優化領域的世界領先專家。他最近的研究興趣包括網絡設計問題、電信優化、電子商務、數據挖掘、生物醫學應用和大規模計算。Panos Pardalos是一位多產的作者，並在世界各地講學。他獲得了眾多獎學金和獎項，其中最近的是2018年的洪堡研究獎。

Andrei Raigorodskii是莫斯科物理技術學院（MIPT）的聯邦數學教授，他是應用數學和計算機科學Phystech學院的主任，離散數學系的負責人，高級組合數學和網絡應用實驗室的負責人，以及應用研究MIPT-Sberbank實驗室的負責人。他還是高加索數學中心的負責人。他在MIPT、MSU和HSE講學，並發表了約200篇論文和20本書。他是《莫斯科組合數學和數論雜誌》的主編。2011年，他獲得了俄羅斯總統科學和創新獎，以表彰他對年輕科學家的貢獻。

Michael Th. Rassias是蘇黎世大學的研究員，也是普林斯頓高等研究院的訪問研究員。在2014年至2015年間，在普林斯頓大學數學系進行博士後研究期間，他與約翰·F·納什合作編寫了《數學中的開放問題》（Springer，2016年）一書。他在數學問題解決競賽中獲得了多個獎項，包括2003年在東京舉辦的國際數學奧林匹克競賽的銀牌。2014年，他獲得了雅典學院的Notara獎。他與Springer合著和編輯了多本書。他目前的研究興趣包括數學分析、解析數論，特別是黎曼猜想、哥德巴赫猜想、質數分布、逼近理論、函數方程和解析不等式。