| CODE | SOR1310 | ||||||||||||
| TITLE | Optimization | ||||||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||||||
| MQF LEVEL | 5 | ||||||||||||
| ECTS CREDITS | 4 | ||||||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||||||
| DESCRIPTION | Introduction to Mathematical Programming - Basic Concepts, Weierstrass Theorem; - Optimality Conditions; - Unconstrained Optimization; - Optimization by Calculus; - Application of Calculus in Classical Inventory Theory; - Line Search Methods; - Introduction to Multivariate Optimization; - Constrained Optimization; - Theorem of Lagrange; - Selected Modelling Techniques; - Converting Models into Linear Form; - Use of Logical Variables; - Use of Simulation in Optimization Problems; - Software Packages. Study-Unit Aims: - Define and describe what a general optimization problem is while providing real life examples that highlight the use and importance of optimization; - Introduce the mathematical foundations of optimization coming from Analysis; - Define the components of an optimization problem and explain the difference between different forms of optimization problems; - Present the theory related to unconstrained and constrained optimization problems; - Bring in the optimality conditions which are necessary for the existence of optimal points; - Illustrate all the above using graphs and plots; Introduce and explain the basic steps that one should follow to apply well-known optimization algorithms, such as: - the uniform Search Method; - the golden section method; - the dichotomous search method, and many more; - The student will be exposed to the theory behind these methods and will learn to use the respective software tools; - Apply the above techniques to specific application examples of great interest. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Formulate certain real life problems into mathematical optimization structure; - find optimal solutions by applying the corresponding optimality conditions; - identify the optimization algorithm which is appropriate for the solution of the given optimization problem; - interpret the results obtained. 2. Skills: By the end of the study-unit the student will be able to: - illustrate graphically a two-dimensional optimization problem; - learn how to apply a number of solution techniques for finding optimal points (if any); - use various software packages (Matlab, Python) to solve basic optimization problems. Main Text/s and any supplementary readings: Suggested Texts: - Apostol, T. M. (1974) Mathematical Analysis, Addison Wesley Publishing Company - Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (1993) Nonlinnear Programming - Theory and Applications, Wiley - Gill, P. E., Murray, W. and Wright, M. H. (1986) Practical Optimization, Academic - Spivak, M. (1994) Calculus, Publish or Perish Inc. - Sundaram, R. K. (1999) A First Course in Optimization Theory, Cambridge University Press - Walker, R. C. (1999) Introduction to Mathematical Programming, Prentice Hall Inc. - Williams, H.P. (1999) Model Building in Mathematical Programming, Wiley |
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| ADDITIONAL NOTES | Pre-requisite Qualification: Advanced Level in Pure Mathematics | ||||||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||||||
| 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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