Max-min eigenvalue problems, primal-dual Interior point algorithms, and Trust region subproblemst
Franz Rendi, Robert J. Vanderbei, Henry Wolkowicz · Optimization methods & software · 1995
Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and efficient. Both algorithms are based on transforming the problem to one with constraints over the cone of positive semidefinite matrices, i.e. Löwner order constraints. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row