624 A HYBRID ALGORITHM FOR OPTIMIZING EIGENVALUES OF SYMMETRIC DEFINITE PENCILS J. Haeberly, M. Overton, February 1993 We present an algorithm 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, 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 which establishes the optimality of the computed solution.