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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Nonlinear Optimization (MATH11244)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryFirst 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 Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) 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)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Understand the theoretical analysis and main results for constrained and unconstrained nonlinear optimization problems,
  2. know the main solution ideas for such problems
  3. assess their advantages and disadvantages for a given problem
  4. apply them to a given problem
  5. Develop and implement such optimization techniques for simple problems
Reading List
Additional Information
Graduate Attributes and Skills Not entered
Study Abroad Some previous exposure to optimization (LPMS or FuO or FuOR)
Course organiserDr Andreas Grothey
Tel: (0131 6)50 5747
Course secretaryMiss Gemma Aitchison
Tel: (0131 6)50 9268
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