We propose an unconstrained minimization framework to symmetric eigenvalue problems in both discrete and continuous settings. The functional to be minimized has the form of a difference of two convex functionals. This functional has an interesting property: all local minimizers are global minimizers. We discuss local and global convergence results by applying the gradient descent method and the Newton’s method to solve the minimization problem. We further provide numerical comparison results as well as an application to a trust-region subproblem.

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