Postgraduate Course: Nonlinear Optimization (MATH11244)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  First and second order optimality conditions for unconstrained optimization
Linesearch and trustregion methods for unconstrained optimization problems (steepest descent, Newton¿s method)
conjugate gradient method
linear and nonlinear leastsquares
First and secondorder optimality conditions for constrained optimization problems; overview of methods for constrained problems (activeset methods, sequential linear and quadratic programming, penalty methods, augmented Lagrangians, filter methods). 
Course description 
The solution of optimal decisionmaking 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 closelyrelated 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.

Course Delivery Information

Academic year 2024/25, Not available to visiting students (SS1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 9,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
71 )

Assessment (Further Info) 
Written Exam
70 %,
Coursework
30 %,
Practical Exam
0 %

Additional Information (Assessment) 
70% Exam
30% Coursework 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Nonlinear Optimization (MATH11244)  2:00  
Learning Outcomes
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

Additional Information
Graduate Attributes and Skills 
Not entered 
Study Abroad 
Some previous exposure to optimization (LPMS or FuO or FuOR) 
Keywords  NlOp 
Contacts
Course organiser  Dr Andreas Grothey
Tel: (0131 6)50 5747
Email: Andreas.Grothey@ed.ac.uk 
Course secretary  Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk 

