TY - JOUR
T1 - Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem
AU - Gong , Siru
AU - Su , Yangfeng
JO - Journal of Computational Mathematics
VL - 6
SP - 1117
EP - 1136
PY - 2023
DA - 2023/11
SN - 41
DO - http://doi.org/10.4208/jcm.2203-m2020-0303
UR - https://global-sci.org/intro/article_detail/jcm/22106.html
KW - Eigenvalue optimization, Multiple eigenvalue, Non-smooth optimization, Implicit determinant method, Crawford number.
AB - <p style="text-align: justify;">Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs. In
this paper, we generalize the implicit determinant method to solve an Hermitian eigenvalue
optimization problem for smooth case and non-smooth case. We prove that the implicit
determinant method converges locally and quadratically. Numerical experiments confirm
our theoretical results and illustrate the efficiency of implicit determinant method.</p>