Lectures:
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization. Augmented Lagrangians
Duality in convex programming. Saddle points.
Non-smooth optimization, subgradients and optimality conditions.
Exercises:
Introduction to Python programming.
Implementation of the golden section and Fibonacci series methods.
Implementation of the Newton-like methods.
Implementation of the gradient-based method.
Implementation of the penalty method for equality constrained minimization.
Implementation of the augmented Lagrangian method.
Solution of selected engineering problems using optimization software.
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization. Augmented Lagrangians
Duality in convex programming. Saddle points.
Non-smooth optimization, subgradients and optimality conditions.
Exercises:
Introduction to Python programming.
Implementation of the golden section and Fibonacci series methods.
Implementation of the Newton-like methods.
Implementation of the gradient-based method.
Implementation of the penalty method for equality constrained minimization.
Implementation of the augmented Lagrangian method.
Solution of selected engineering problems using optimization software.