Algorithms for Linear-quadratic Optimization

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Summary: Algorithms for Linear-quadratic Optimization
Review: 2.1.1 Newton's method 98
2.1.2 Stabilization methods 101
2.2 Computation of Real Schur Form and Invariant Subspaces 105
2.2.1 Basic definitions and properties 105
2.2.2 Preprocessing algorithms 114
2.2.3 The QR algorithm 118
2.2.4 Real Schur form computation and ordering 135
2.3 Solving Sylvester and Lyapunov Equations 143
2.3.1 Solving Sylvester equations 144
2.3.2 Solving Lyapunov equations 159
2.3.3 Solving stable non-negative definite Lyapunov equations 162
2.4 Stabilization Algorithms 174
2.4.1 Full stabilization algorithms 174
2.4.2 Partial stabilization algorithms 177
2.5 Newton-Based Riccati Solvers 179
2.5.1 Algorithmic templates 180
2.5.2 Computational issues 183
2 5.3 Applicability and limitations 186
References 191
3 Schur and Generalized Schur Algorithms 197