Finite-dimensional optimization (over continuous variables)
- Unconstrained Optimizations (iterative methods)
- Minimizing quadratic functions, least square minimization
- Gradient descent. Backtracking
- Steepest descent
- Newton, quasi-Newton, cubic-Newton methods
•Equality Constrained Minimization. Primal-dual Newton method.
•Interior Point Methods
•Linear Programming. Simplex Method.
•L1-regularization. Sparsity. Compressed Sensing.
Optimal Control (example of Infinite-dimensional optimization). Dynamic Programming.
Bonus: Oscillation phenomena. ”Structural" conditions to guarantee that numerical discretizations faithfully capture a continuous problem.