# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2024/2025

### Timetable information in the Course Catalogue may be subject to change.

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# 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 Not available to visiting students SCQF Credits 10 ECTS Credits 5 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 constrained optimization problems; overview of methods for constrained problems (active-set methods, sequential linear and quadratic programming, penalty methods, augmented Lagrangians, filter methods). Course description 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 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. 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.
 Pre-requisites Students MUST have passed: ( Introduction to Linear Algebra (MATH08057) AND Several Variable Calculus and Differential Equations (MATH08063)) OR ( Accelerated Algebra and Calculus for Direct Entry (MATH08062) AND Several Variable Calculus and Differential Equations (MATH08063)) OR Linear Algebra and Several Variable Calculus (PHYS08042) Co-requisites Prohibited Combinations Other requirements Open to any School of Mathematics PGT programme. Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
 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
 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 problemsassess their advantages and disadvantages for a given problemapply them to a given problemDevelop and implement such optimization techniques for simple problems
 None
 Graduate Attributes and Skills Not entered Study Abroad Some previous exposure to optimization (LPMS or FuO or FuOR) Keywords NlOp
 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
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