For more information, see Announcements for current students and course outline

- Aims
- Outline
- References
- Prerequisites
- Schedule for Winter 2024
- Marking scheme for Winter 2024
- Announcements for current students

- Review the basic concepts in numerical optimization.
- Introduce numerical methods for solving continuous (mostly unconstrained) optimization problems.
- Evaluate numerical optimization methods with respect to their accuracy, convergence, time and memory complexities.
- Develop and practice computer skills in implementing numerical optimization methods efficiently on the computer, as well as skills to judge the correctness of numerical results.
- Use high level software for studying numerical optimization methods.

- Introduction, continuous vs discrete, unconstrained vs constrained, global and local minima, general considerations
- (1D optimization) Golden section search, Newton's
- Line search methods
- Trust region methods
- Conjugate gradient methods
- Quasi-Newton'smethods
- Approximating derivatives, the gradient, the Jacobian, the Hessian

Numerical Optimization |
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Jorge Nocedal and Steven Wright | Numerical Optimization | Springer NY, 2006 |

General Numerical Analysis |
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Michael Heath | Scientific Computing: an introductory survey | SIAM 2018 or McGraw-Hill Inc. 2002+ |

- Courses: a numerical methods course (e.g. csc336), a multivariate calculus course (e.g. mat235, mat237), a linear algebra course (e.g. mat221, mat223, mat240).
- General: Ability to handle notation and to do algebraic manipulation. Fluency in matrix and vector manipulation.
- Calculus: Differentiation and integration of polynomial, trigonometric, exponential, logarithmic and rational functions, continuity, limits, graphs of functions, Taylor series, Rolle's theorem, mean-value theorem, de l' Hospital's rule, partial derivatives, gradient, multi-dimensional Taylor series
- Linear Algebra: Matrix and vector addition and multiplication, elementary row operations, linear (in)dependence, inverse matrix, banded and sparse matrices, properties of matrices, matrix norms, condition numbers, eigenvalues, eigenvectors, various decompositions, etc
- Programming: strong coding abilities in some programming language, such as MATLAB, C or FORTRAN.
- Other Mathematics: induction.

Lectures | Tuesday 3-5 PM | Room MP 134 |

Tutorial | Thursday 3-4 PM | Room MP 134 |

Office Hours | Wednesday 1-2 PM | Room BA 4226 or online |

We may not use all tutorial times.

** Tentative marking scheme for Winter 2024 **

Problem set 1 | 20% |

Problem set 2 | 22.5% |

Problem set 3 | 22.5% |

Term test 1 | 35% |