Full title: Optimizations with orthogonality constraints and eigenvector-dependent nonlinear eigenvalue problems. Join us for ASE-60, where we celebrate the life and the career of Professor Alan Stuart Edelman, on the occasion of his 60th birthday: https://math.mit.edu/events/ase60celebration/
Optimizations with orthogonality constraints are ubiquitous in scientific computing, such as finding projection matrices for dimensionality reduction in high dimensional data analysis and energy minimization for electronic structure calculations. Edelman, Arias and Smith's 1998 paper on the geometry of algorithms with orthogonality constraints is a seminal work that has a great influence in the fields of optimizations and numerical linear algebra over two decades. We will present recent development of optimization with orthogonality constraints from the perspective of algebraic nonlinear eigenvalue problems with eigenvector dependency (NEPv). This is a joint work with Ren-Cang Li of University of Texas, Arlington and Ding Lu of University of Kentucky.