Functional Optimization

Functional Optimization

  1. 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
     
  2.  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