MA5895 Numerical Optimization

Course Details

Introduction (1 lecture), Background and Classification of optimisation problems (1 lecture), Unconstrained optimisation (2 lectures), Line Search methods (3 lectures), Trust region methods (3 lectures), Gradient descent (2 lecture), Exact and Quasi-Newton Methods (5 lectures), Non-linear least squares (1 lecture), Nonlinear equations (2 lectures), Constrained optimization (3 lectures), Linear programming: Simplex method (2 lectures); Nonlinear constrained optimization (1 lecture), Farkas' lemma (1 lecture), Karush–Kuhn–Tucker (KKT) conditions (2 lectures), Quadratic programming (2 lectures), Penalty, Barrier and Augmented Lagrangian methods (4 lectures), Sequential Quadratic Programming (2 lectures), Large scale optimization: Algorithms and Softwares (4 lectures).

Course References:

1. Jorge Nocedal & Stephen J. Wright, Numerical Optimization, Publisher : Springer
2. R. Fletcher, Practical Methods of Optimization, Publisher: Wiley
3. D. Bertsekas, Nonlinear Programming, Athena Scientific.
Reference Books:
1. P. E. Gill, W. Murray and M. H. Wright, Numerical Methods for Linear Algebra and Optimization: Volume 1, Addison-Wesley.
2. P. E. Gill and W. Murray, Numerical Methods for Constrained Optimization, Academic Press. 3. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, Academic Press.