Functional Optimization
- Calculus of Variations
i.Examples
ii.Euler-Lagrange equations
iii. Phase-Space intuition and relation to optimization
iv. Towards numerical solutions of the Euler-Langrange equations (bonus)
v. Dependence of the action on the end-points
vi. Variational principle of classical mechanics
vii. Legendre-Fenchel transform (bonus)
viii. Second variations (bonus)
ix. Methods of Lagrange Multipliers
- Optimal Control and Dynamic Programming
i. Linear quadratic control via calculus of variations (bonus)
ii. From variational calculus to Hamilton-Jacobi-Bellman equations
iii. Pontryagin minimal principle
iv. Dynamic programming in optimal control and beyond
v. Dynamic programming in discrete mathematics