Mathematical Optimization

    Course Code: 
    8116
    Semester: 
    4th
    Compulsory Courses
    Professor: 

    AVGERINOS IOANNIS

    Course Description

    The course examines the theory and algorithms of Mathematical Optimization, as well as their relationship with other fields (such as Game Theory). Specifically, the optimization of linear problems, Dual Theory, basic Linear Programming algorithms, basic concepts of Non-Linear Programming and Integer Programming, problem formulation, Dynamic Programming, and the relationship of Linear Programming to Game Theory are examined.

    The course material includes the following topics:

    • Elements of Linear Algebra, parametric solution of linear equations
    • The Simplex Method: description, geometric interpretation and special cases
    • Sensitivity analysis and economic meaning
    • The Karush-Kuhn-Tucker conditions, description and proof
    • Duality Theory
    • Introduction to Non-Linear Programming
    • The transportation problem and the Network Simplex Algorithm
    • Model building and formulation, applications and case-studies
    • Integer Programming, modeling and solution methods
    • Linear Programming and Game Theory
    • Dynamic Programming: formulations, solution approach and applications

    Learning Outcomes

    The aim is to understand the above and their combined application to optimization problems as they arise from practical applications. Sub-objectives are to deepen the understanding of mathematical structures and properties of problem categories, the use of Mathematical Optimization algorithms and the design of their variants for special cases of problems and the formulation and solution of relevant practical problems.