Non Linear Optimization
Code
10808
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Paula Alexandra da Costa Amaral
Weekly hours
2
Teaching language
Português
Objectives
The goals are:
1- To distinguish the problems by degree of difficulty.
2 - To know optimality conditions and methods for local optima.
3- To understand how the methods "work" for problems with and without constraints, and to be able to compare their merits and weaknesses and convergence rate.
4- To understand the application of some methods for special problems like least squares.
5- To be have an overview of global optimization methods.
Prerequisites
Linear Optimization and Calculus.
Subject matter
1- Introduction
- Formulation of problems
- graphical resolution of simple problems
- Rates of convergence
2 Unconstrained Problems
- Necessary and sufficient optimality conditions
- Newton method and gradient descent .
- Line search methods.Armijo and Wolfe conditions
- Trust region methods.
- Quasi-Newton methods.The BFGS formula.
3 Constrained optimisation
- Necessary and sufficient optimality conditions
- Active set method
- Lagrangean Dual
- KKT conditions
4 Quadratic Programming.
5 Penalities, Barrier and augmented Lagrangian methods.
6 Least Squares Problems
7 Brief introduction to global optimization.
Bibliography
Bertsekas, Dimitri P. (1995) - “Nonlinear Programming”,Athena Scientific;
Nash, Stephen G.; Sofer, Ariela, (1996) – “Linear and Nonlinear Programming”, McGraw-Hill;
Nocedal, Jorge; Wright, Stephen J., (1999) – “Numerical Optimization”, Springer-Verlag.