| 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 | 鈥� Convex analysis - Convex sets; - Convex functions; - Relaxations of convexity. 鈥� Unconstrained optimization - Optimality conditions; - Search methods with and without the use of derivatives. 鈥� Constrained optimization - Geometric and algebraic optimality conditions; - Search methods for problems with constraints. 鈥� 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. |
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| ADDITIONAL NOTES | Pre-requisite Study-units: SOR1310, SOR1320 | ||||||||||||
| STUDY-UNIT TYPE | Lecture and Practical | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Maria Kontorinaki |
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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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