Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem

Abstract

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.