Riemannian Newton and conjugate gradient algorithm for computing Lagrangian invariant subspaces ∗
نویسنده
چکیده
The computation of Lagrangian invariant subspaces of a Hamiltonian matrix, or the closely related task of solving algebraic Riccati equations, is an important issue in linear optimal control, stochastic control and H∞-design. We propose a new class of Riemannian Newton methods that allows to compute isolated Lagrangian invariant subspaces of a Hamiltonian matrix. The algorithm implements a variant of the Newton method for a quadratic vector field on the Lagrange Graßmann manifold. It yields new methods to solve the algebraic Riccati equation in linear optimal control. In addition, an intrinsic conjugate gradient algorithm on the Lagrangian Grassmanian is introduced.
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