sphere constraint – Optimization Online

A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold

Published: 2013/01/01, Updated: 2013/12/25

Applications - Science and Engineering, Nonlinear Optimization adaptive nonmonotone line search, barzilai-borwein-like method, feasible, global convergence, heterogeneous quadratic functions, kohn-sham total energy minimization, low-rank correlation matrix, null space, orthogonality constraint, range space, sphere constraint, stiefel manifold

This paper considers optimization problems on the Stiefel manifold $X^TX=I_p$, where $X\in \mathbb{R}^{n \times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $X$ and the null space of $X^T$. While this general framework … Read more