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 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).
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 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)
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 programme where it appears on the Degree Programme Table (DPT). 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.

Course Delivery Information

Academic year 2025/26, 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		Minutes
Main Exam Diet S2 (April/May)	Nonlinear Optimization (MATH11244)		120

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