TL;DR
This paper explores recent advances in nonlinear algebra and critical point equations, emphasizing the importance of going beyond traditional linear algebra in model design and numerical algorithms for optimization and PDEs.
Contribution
It highlights the role of nonlinear algebra in optimization, statistics, and linear PDEs, expanding the mathematical toolkit beyond linear algebra.
Findings
Advances in critical point equations for optimization and statistics
Role of nonlinear algebra in linear PDE analysis
Encourages thinking beyond linear algebra in model design
Abstract
Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of Mathematicians 2022. It covers recent advances in the study of critical point equations in optimization and statistics, and it explores the role of nonlinear algebra in the study of linear PDE with constant coefficients.
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