Introduction to Nonlinear Programming/Optimization

14 dezembro 2010, 16:30 • Fernando De Oliveira Durão

Solution of 2 problems:

1. Optimality conditions verification (stopping criteria), descent directions and directional derivative

2. Exact minimization of real function (phi) of a (positive) scalar variable alpha: first and second order conditions

Introduction to Nonlinear Programming/Optimization

14 dezembro 2010, 15:30 • Fernando De Oliveira Durão

1. Introduction to algorithms of unconstrained optimization

1.1 Specific algorithms (Presentation with animated demos)

1.1.1 Gradient-based (Steepest descent and Nonlinear Conjugate Gradient Methods)

1.1.2 Newton-type methods

(Convex) Local quadratic models (second order approximation and modifications):Modified Cholesky factorization and Levenberg-Marquardt correction (connections to restricred step methods). Quasi-Newton methods

1.2 Approximate/Soft Line Search methods

1.2.1 Weak Wolfe conditions (sufficient decrease and curvature conditions)

1.2.2 Strong Wolfe conditions (sufficient decrease and curvature conditions)

1.2.3 Goldstein conditions

Introduction to Nonlinear Programming/Optimization

13 dezembro 2010, 17:00 • Fernando De Oliveira Durão

Solution of 2 problems:

1. Optimality conditions verification (stopping criteria), descent directions and directional derivative

2. Exact minimization of real function (phi) of a (positive) scalar variable alpha: first and second order conditions

Introduction to Nonlinear Programming/Optimization

13 dezembro 2010, 16:00 • Fernando De Oliveira Durão

1. Introduction to algorithms of unconstrained optimization

1.1 Sequences of approximations in R ⁿ (Convergence and Rate of Convergence, Stopping criteria)

1.2 Direct Methods (Simulated Annealing, Genetic Algorithms,  Nelder & Mead simplex method)

1.3 Indirect Methods

1.3.1 Line Search based methods (Search along descent directions)

1.3.2 Trust-Region (Restricted Step) methods

Introduction to Nonlinear Programming/Optimization

7 dezembro 2010, 16:30 • Fernando De Oliveira Durão

Solution of two problems:

1. Taylor theorem: First and second order approximations.

2. Determination and classification of stationary points.