Dynamic Optimization

• To apply the Euler-Lagrange equation to identify stationary points for integral functionals
• To apply the Maximum Principle of Pontryagin to identify optimal controls.
• To pose and solve the Dynamic Programming equation for optimal control of differential equations.
• To compute linearized feedback strategies which apply near optimal equilibria and trajectories.
• To pose and solve the Dynamic Programming equation for Markov Decision Problems and optimization problems on graphs
• To analyze two-player and mean-field dynamic games
• To analyse dynamic optimization problems both theoretically and numerically
• To give examples of dynamic optimization problems in physics, decision, and control

Optimization over function spaces; calculus of variations. Pontryagin’s maximum principle; Hamiltonian formalism. Dynamic programming on graphs. Markov Decision Problems. The Hamilton-Jacobi-Bellman equation for optimal control. Dynamic games; mean-field games. Numerical methods for optimal control.

01617, Dynamic systems (e.g. 01617). Optimization including constrained optimization and Lagrange multipliers (e.g. 02612). Some exposure to partial differential equations will be helpful (e.g. 01418). Elementary probability is needed and exposure to Markov chains is helpful (e.g. 02407).

Lectures. Exercises. methods

Maximum: 40.

Please be aware that this course has a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.