Postgraduate Course: Nonlinear Optimization (MATH11031)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | The solution of optimal decision-making and engineering design problems in which the objective and constraints are nonlinear functions of potentially (very) many variables is required on an everyday basis in the commercial and academic worlds. A closely-related subject is the solution of nonlinear systems of equations, also referred to as least-squares or data fitting problems that occur in almost every instance where observations or measurements are available for modelling a continuous process or phenomenon, such as in weather forecasting. The mathematical analysis of such problems and study of the classical methods for their solution are fundamental for understanding both practical methods of solution and the nature of the solution which may be obtained. Thus it imparts knowledge and insight into the optimal choice of available methods (software) or ability to develop such techniques for the practical problems at hand.
Aims :
- To introduce the analysis of nonlinear optimization problems.
- To present the classical methods for solving nonlinear optimization problems with and without constraints, and nonlinear equations.
Syllabus summary:
Linesearch and trust-region methods for unconstrained optimization problems (steepest descent, Newton's method); conjugate gradient method; linear and nonlinear least-squares. First- and second-order optimality conditions for constrained optimization problems; overview of methods for constrained problems (active-set methods, sequential quadratic programming, interior point methods, penalty methods, filter methods). |
| Course description |
Not entered
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
| Understanding the construction and main solution ideas for nonlinear optimization problems. Ability to assess the quality of available methods and solutions for such problems, as well as to potentially develop such optimization techniques and implementations.
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Contacts
| Course organiser | Dr Sergio Garcia Quiles
Tel: (0131 6)50 5038
Email: Sergio.Garcia-Quiles@ed.ac.uk |
Course secretary | Mrs Frances Reid
Tel: (0131 6)50 4883
Email: f.c.reid@ed.ac.uk |
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