Some topics: dynamic programming, Hamilton-Jacobi-Bellman equations, viscosity solutions, dual problems, computational complexity, numerical methods for Hamilton-Jacobi equations, symplectic methods.
Some applications: optimal portfolio (SDE), American options (SDE), catalytic converter (PDE), shape optimization (PDE).
Goal: to understand and be able to use basic mathematical and numerical methods to solve optimal control problems based on differential equations, which includes that the student after the course can:
derive the Hamilton-Jacobi-Bellman equation,
derive the Pontryagins principle,
formulate and derive existence and uniqueness of viscosity solutions,
analyze computational complexity for dynamics programming and Lagrange’s method,
formulate and analyze numerical methods for Hamilton-Jacobi equations,
formulate applications of optimal control, e.g. for inverse problems,
analyze and use symplectic numerical methods for Hamiltonian systems.
A Master degree including at least 30 university credits (hp) in in Mathematics (including differential equations and numerical analysis).
L.C. Evans, Partial Differential Equations, Oxford
Lecture notes on SDE, PDE and numerics
If the course is discontinued, students may request to be examined during the following two academic years.
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework
Computer lab
Written exam
Home assignments completed
Written exam completed
