| Center |
| Faculty of Mathematics |
| Departament |
| Statistics and Operational Research |
| Lecturers in charge |
| Sin datos cargados |
| Met. Docent |
| In the theoretical classes the teacher will introduce the concepts and methods of Non Linear Programming, with examples and exercises to be solved by the students. In the practical classes the students will model linear problems, solved them with available codes and interpret the results. |
| Met. Avaluació |
| In a written final test the students will be asked to solve problems and answer questions related to the theoretical part of the subject. 80% of ther marks will be awarded for the theoretical part and the remaining 20% for the practical part. |
| Bibliografia |
| Barbolla R., Cerdá, E. Y Sanz, P. Optimización. Cuestiones, ejercicios y aplicaciones a la economía . Prentice Hall 2001. Bazaraa, M.S., Sherali, D.S. and Shetty, C.M., Nonlinear Programming. Theory and Algorithms. 2ª edición. John Wiley, 1993. Bertsekas, D.P., Nonlinear Programming, Athena Scientific, Belmont, 1995. Eppen, G.D. et al, Investigación de Operaciones en la ciencia administrativa, 5ª edición, Prentice Hall, 2000. Luenberger, D.E., Programación lineal y no lineal. Addison.Wesley Iberoamericana, 1989. Nocedal, J, and Wright, S. Numerical optimization. Springer-Verlag New York, 1999. Peressini, A.L., Sullivan, F.E. and Uhl, J.J., The Mathematics of Nonlinear Programming. Springer Verlag, 1988. |
| Continguts |
| 1.- Unconstrained optimization. Optimality conditions. Descent methods. Gradient methods. Newton method. Conjugate direction Methods. Quasi-Newton Methods. 2.- Optimization over a convex set. Optimality Conditions. Feasible Directions. Gradient Projection Methods. Manifold Suboptimization. Quadratic Programming. 3.- Lagrange Multiplier Algorithms. Necessary conditions for Equality Constraints. Sufficient Conditions. The Augmented Lagrangian function. Inequality Constraints: Karush, Kuhn and Tucker Conditions. 4.-Penalty Methods. Barrier Methods. Penalty and Augmented Lagrangian Methods. Sequential Quadratic Programming. Lagrange-Newton Methods. |
| Objetius |
| To introduce the students to the Non-Linear programming formulations and to the problem of characterising the optimality of the obtained solutions. To introduce the students to the optimization methods which would allow them to solve the most common non-linear problems. |
| URL de Fitxa |