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Numerical Analysis and Optimization

Schedule

Monday, 4 November 2019 to Friday, 6 March 2020
Total hours: 40
Hours of lectures: 40

Examination procedure

  • Written test
  • oral exam

Prerequisites

The corse is suitable for those students who have had a first introductory course on numerical methods but have not yet been exposed to systematic courses on Numerical Linear Algebra and Optimization.

Syllabus

Part I, Computational Methods of Linear Algebra

Review of basic facts from linear algebra.

Matrix norms.

Stability and conditioning in Numerical Linear Algebra.

Matrix Factorizations (LU, Cholesky, QR...).

Direct and Iterative methods for solving linear systems.

Computation of eigenvalues and eigenvector of matrices.

Least squares problems, the Moore-Penrose pseudoinverse, singular value decomposition.

 

Part II, Methods of Numerical Optimization

Unconstrained optimization:

-Gradient descent, Newton and Quasi-Newton methods.

-Globalization techniques.

Constrained optimization:

-Penalty methods.

-Method of Lagrange multipliers, augmented Lagrangian methods.

-KKT systems. 

 

 Educational Goal: 

The goal of this course is to provide the students the basic tools of numerical linear algebra and of optimization (both constrained and unconstrained).

The emphasis will be on the fundamental concepts (in particular those of stability and conditioning of problems) and on the algorithmic aspects. 

 

 

Bibliographical references

References will be provided in the course of the lectures.