Sumários
10 janeiro 2025, 10:30
•
Jorge Tiago
Farkas lemma.
The critical cone. Second-order necessary conditions and second-order sufficient conditions. Convexity-based first-order sufficient conditions.
Using the Newton method to identify KKT pairs.
Penalty methods, The quadratic penalty approach for equality and inequality constrained optimization problems.
Convergence and properties of the quadratic penalty method.
8 janeiro 2025, 17:30
•
Jorge Tiago
Examples.
The LICQ and the equivalence between the tangent cone and the linearized feasible directions.
Examples.
Tangent cone and necessary conditions for optimality.
6 janeiro 2025, 08:00
•
Jorge Tiago
Optimization with inequality and equality constraints. Feasible and active set.
Linear independence constraint qualification. The Karush-Khun-Tucker conditions.
Examples.
20 dezembro 2024, 10:30
•
Jorge Tiago
Convergence of the Newton method for optimization.
Quasi-Newton methods.
Derivation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Properties and convergence.
Sherman-Morrison based formula for the update of the inverse of the Hessian approximation in BFGS.
16 dezembro 2024, 08:00
•
Jorge Tiago
The steepest descent method. Properties of the steepest descent method for quadratic functions.
General convergence properties. The Newton method for optimization.
