Optimization (Algorithms)

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.