High-Dimensional Optimization and Probability (eBook)

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.