Optimizing eigenvalues of symmetric definite pencils

We consider the following quasiconvex optimization problem: minimize the largest eigenvalue of a symmetric definite matrix pencil depending on parameters. A new form of optimality conditions is given, emphasizing a complementarity condition on primal and dual matrices. Newton´s method is then applied to these conditions to give a new quadratically convergent interior-point method which works well in practice. The algorithm is closely related to primal-dual interior-point methods for semidefinite programming.