The course introduces the basic concepts of optimization and the different types of optimization problems, the iterative algorithms to solve these problems, and their properties. The practice of optimization using modeling languages to describe a problem and commercial and publicly available solvers is also emphasized.
(veure versió en anglès)
Competències relacionades:
CEE5.3,
CEE3.2,
CEE3.3,
(veure versió en anglès)
Competències relacionades:
CEE5.3,
CTR6,
Continguts
Optimització sense restriccions
Optimality conditions. Convexity. Descent directions.
Line search. Acceptability of step sizes.
General minimization algorithm.
Gradient method. Rate of convergence.
Newton's method. Factorizations to ensure convergence.
Weighted least squares.
Introduction to AMPL. The Neos solver site.
Optimització amb restriccions i "Support Vector Machines".
- Introduction to Support Vector Macines (SVM)
- KKT Optimality conditions of constrained optimization. Optimality conditions of SVM.
- Duality in Optimization. The dual of the SVM.
Programació Entera.
- Modelling problems with binary variables.
- The branch and bound algorithm for integer programming
- Gomory's cutting planes algorithm.
- Minimal spanning tree problem and algorithms of Kruskal and Prim.
Activitats
ActivitatActe avaluatiu
Unconstrained Optimization
Optimality conditions. Convexity. Descent directions.
Line search. Acceptability of step sizes.
General minimization algorithm.
Gradient method. Rate of convergence.
Newton's method. Factorizations to ensure convergence.
Weighted least squares.
Introduction to AMPL. The Neos solver site. Objectius:1234
Teoria
17.3h
Problemes
0h
Laboratori
0h
Aprenentatge dirigit
0h
Aprenentatge autònom
35h
Constrained Optimization and Support Vector Machines
- Introduction to Support Vector Macines (SVM)
- KKT Optimality conditions of constrained optimization. Optimality conditions of SVM.
- Duality in Optimization. The dual of the SVM. Objectius:1234
Teoria
17.4h
Problemes
0h
Laboratori
0h
Aprenentatge dirigit
0h
Aprenentatge autònom
35h
Integer Programming
- Modelling problems with binary variables.
- The branch and bound algorithm for integer programming
- Gomory's cutting planes algorithm.
- Minimal spanning tree problem and algorithms of Kruskal and Prim Objectius:1234