This course requires an understanding of basic concepts of linear programming and its objective is to introduce the students to the key methodologies of non-linear and dynamic programming. The focus is on understanding various optimization techniques and on learning the theory upon which these techniques rely. After the end of the class, the students will be familiar with the development of the necessary skills for formulating related problems, using advanced tools to solve them, and comparing alternative solutions.

• Review of linear programming.
• Introduction to nonlinear programming – Convexity of functions and sets.
• Problems without constraints.
• Problems with constraints.
• Lagrange multipliers – Karush Kuhn
• Tucker optimality conditions.
• Dynamic Programming – The Principle of Bellman Optimality conditions.
• Problems with a finite horizon – Problems with an infinite horizon.

Suggested Literature:

• Βασιλείου Π.Χ., Γεωργίου Α. (1996). Μη Γραμμικές Μέθοδοι Βελτιστοποίησης. Εκδόσεις Ζήτη,
  Θεσσαλονίκη.
• Λυμπερόπουλος Γ, Ζηλιασκόπουλος Α. (2005). Θεωρία Βελτιστοποίησης. Πανεπιστημιακές Σημειώσεις, Πανεπιστημιακές Εκδόσεις Θεσσαλίας.
• Ξηρόκωστας Δ. (1999). Επιχειρησιακή Έρευνα ‐ Μη Γραμμικός και Δυναμικός Προγραμματισμός. Εκδόσεις Συμμετρία, Αθήνα.
• Hillier F.S., Lieberman G.J. (2001). Introduction to Operations Research. McGraw‐Hill.
• Taha H., (2011). Introduction to Operations Research. Μετάφραση στα ελληνικά, Εκδόσεις Α. Τζιόλα & Υιοί Ο.Ε.
• Winston W.L., Venkataramanan M.(2002). Introduction to Mathematical Programming. Duxbury Press

Related Academic Journals:

‐ Annals of Operations Research
‐ Computational Optimization and Applications
‐Computers and Industrial Engineering
‐ Computers and Operations Research
‐ Discrete Optimization
‐ Engineering Optimization
‐ European Journal of Industrial Engineering
‐ European Journal of Operational Research
‐ INFORMS Journal on Computing
‐ International Transactions in Operational Research
‐ Journal of Global Optimization
‐ Journal of Industrial and Management Optimization
‐ Journal of Optimization Theory and Applications
‐ Journal of the Operational Research Society
‐ Management Science
‐ Mathematical and Computer Modelling
‐ Mathematical Methods of Operations Research

Greek

Lectures and Practical Exercises