Introductory Optimization Dynamics : Optimal Control with Economics and Management Science Applications

1 Introduction -- 2 The Calculus of Variations -- 3 Boundary Conditions in Variational Problems -- 4 Second Variations and Sufficiency Conditions -- 5 Optimal Control: The Variational Approach -- 6 Constrained Optimai Control Problems -- 7 Linear Optimal Control -- 8 Stabilization Control Models -- 9 Discrete Control Systems -- 10 Sensitivity Analysis -- 11 Some Economic and Management Applications -- Mathematical Appendix: Review Of Differential And Difference Equations -- A.1 Introduction -- A.2 Differential Equations -- A.2.1 First Order Linear Differential Equation Systems -- A.2.2 Fundamental Matrix -- A.2.3 The nth Order Differential Equation -- A.2.4 Non-Homogeneous First Order Differential Equation Systems -- A.3 Difference Equations -- A.4 Stability of Differential and Difference Equations -- A.5 Phase Diagrams and Non-Linear Differential Equations -- A.6 Isoclines -- A.7 Non-Linear Differential Equations -- A.8 Phase Diagrams of Difference Equations -- A.9 Liapunov’s Second (or Direct) Method -- References.