Non Linear Optimization
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.
General characterization
Code
10808
Credits
6.0
Responsible teacher
Paula Alexandra da Costa Amaral
Hours
Weekly - 3
Total - Available soon
Teaching language
Português
Prerequisites
Linear Optimization and Calculus.
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.
Teaching method
Available soon
Evaluation method
The evaluation will be done through two presential exams (one in the middle of the semester and the other one at the end) and several homework assignments (approximately 6), each one including a theoretical and a practical part.
Each exam represents 30 percent of the final grade, and the average of the homework assigments represents the remaining 40 percent.
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.