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Study-Unit Description

Study-Unit Description


CODE SOR2330

 
TITLE Nonlinear Programming

 
UM LEVEL 02 - Years 2, 3 in Modular Undergraduate Course

 
MQF LEVEL 5

 
ECTS CREDITS 4

 
DEPARTMENT Statistics and Operations Research

 
DESCRIPTION • Convex analysis

- Convex sets;
- Convex functions;
- Relaxations of convexity.

• Unconstrained optimization

- Optimality conditions;
- Search methods with and without the use of derivatives.

• Constrained optimization

- Geometric and algebraic optimality conditions;
- Search methods for problems with constraints.

• Lagrange duality

Study-unit Aims:

This study-unit covers Nonlinear Programming at intermediate level. Nonlinear Programming is the basis of many optimization algorithms. This study-unit extends the study-unit of Optimization, taught in Year 1, by introducing more advanced concepts in convex theory, unconstrained and constrained optimization theory, and Lagrange duality.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:

- Explain the concepts of convex sets and convex/concave functions;
- Choose the necessary and/or sufficient conditions that are appropriate for the optimization problem that they need to solve;
- Identify the algorithm(s) that can solve a specific optimization problem.

2. Skills:

By the end of the study-unit the student will be able to:

- Prove that a set is convex (or not) using the definition or by making use of specific theoretical results;
- Characterize the (generalized) convexity/concavity of a function using the definition or by making use of specific theoretical results;
- Apply certain necessary and sufficient conditions on specific optimization problems to locate optimal points analytically;
- Apply an appropriate optimization algorithm to solve a given optimization problem numerically;
- Write a code that applies a specific optimization algorithm to any given function.

Main Text/s and any supplementary readings:

- Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (2006) Nonlinear Programming - Theory and Algorithms, John Wiley & Sons.
- Luenberger, D.G., Ye, Y. (2008) Linear and Nonlinear Programming, Addison-Wesley.
- Bertsekas, D.P. (1999) Nonlinear Programming, Athena Scientific.
- Bazaraa, M.S., Jarvis, J.J. and Sherali, H.D. (2004) Linear Programming and Network Flows, John Wiley & Sons.
- Gill, P.E., Murray, W. and Wright, M.H. (1986) Practical Optimization, Academic.
- Sundaram, R.K. (1999) A First Course in Optimization Theory, Cambridge University Press.
- Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (1993) Nonlinnear Programming - Theory and Applications, John Wiley & Sons.
- Peressini, A.L., Sullivan, F.E. and Uhl, J.J. (1988) The Mathematics of Non-linear Programming, Springer.
- Nocedal, J., Wright, S.J. (2006) Numerial Optimization, Springer.

 
ADDITIONAL NOTES Pre-requisite Study-units: SOR1310, SOR1320

 
STUDY-UNIT TYPE Lecture and Practical

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Computer-Assisted Examination (1 Hour and 30 Minutes) SEM1 Yes 50%
Project SEM2 Yes 50%

 
LECTURER/S Maria Kontorinaki

 

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years.

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