Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem (Journal of Computational Mathematics, 2023)
Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs. Inthis paper, we generalize the implicit determinant method to solve an Hermitian eigenvalueoptimization problem for smooth case and non-smooth case. We prove that the implicitdeterminant method converges locally and quadratically. Numerical experiments confirmour theoretical results and illustrate the efficiency of implicit determinant method.
Keywords: Eigenvalue optimization; Multiple eigenvalue; Non-smooth optimization; Implicit determinant method; Crawford number.