1. Mathematical Programming models: introduction and first definitions
Convex Programming (no local non global minima)
Optimality conditions for unconstrained optimization and constrained optimization.
Special cases: convex feasible set, linear constraints, box constraints. Karush-Kuhn-Tucker conditions
Unconstrained Optimization Algorithms: exact line search, Armijo line search. Gradient method.
2. Algorithms for Constrained Optimization Problems with convex feasible set
Frank wolfe method
Projected gradient method
3. Algorithms for Constrained Optimization with general constraints
Sequential penalty method
Exact penalty functions
Exact Augmented Lagrangian
4. Quadratic Programming
Wolfe duality theory
An application: training of a Support Vector Machine (SVM)
Hints on decomposition methods for SVM