Postgraduate Course: Nonlinear Optimization (MATH11244)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|Summary||First and second order optimality conditions for unconstrained optimization
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 linear and quadratic programming, penalty methods, augmented Lagrangians, filter methods).
The solution of optimal decision-making and engineering design problems in which the objective and/or constraints are nonlinear functions of potentially (very) many variables is required on an everyday basis in the commercial and academic worlds. While often an (easy to solve) linear approximation of the problem suffices, there are many real world applications where the governing equations are truely nonlinear.
A closely-related subject is the solution of nonlinear systems of equations, also referred to as leastsquares 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.
This course will analyse the solution of nonlinear optimization problems both from a theoretical and practical point of view. The theoretical part will as much as possible try to steer away from ¿dry¿ proofs,
but rather attempt to impart (often geometrical) insight into important concepts. The practical part will give a comprehensive overview of classical and modern algorithms for nonlinear optimization.
The course is teamed up with computing labs which form an integral part of the course and allow students to gain first hand experience of the behaviour (advantages and inherent difficulties) of many of the studied algorithms.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2023/24, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 9,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||2:00|
On completion of this course, the student will be able to:
- Understand the theoretical analysis and main results for constrained and unconstrained nonlinear optimization problems,
- know the main solution ideas for such problems
- assess their advantages and disadvantages for a given problem
- apply them to a given problem
- Develop and implement such optimization techniques for simple problems
|Graduate Attributes and Skills
||Some previous exposure to optimization (LPMS or FuO or FuOR)
|Course organiser||Dr Andreas Grothey
Tel: (0131 6)50 5747
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268