A Hybrid Algorithm for Optimizing Eigenvalues of Symmetric Definite Pencils
Jean-Pierre A. Haeberly, Michael L. Overton · SIAM Journal on Matrix Analysis and Applications · 1994
An algorithm is presented for the optimization of the maximum eigenvalue of a symmetric definite pencil depending affinely on a vector of parameters. The algorithm uses a hybrid approach, combining a scheme based on the method of centers, developed by Boyd and El Ghaoui [Linear Algebra Appl., 188 (1993), pp. 63–112], with a new quadratically convergent local scheme. A convenient expression for the generalized gradient of the maximum eigenvalue of the pencil is also given, expressed in terms of a dual matrix. The algorithm computes the dual matrix that establishes the optimality of the computed solution.