Optimization is an area of mathematics that studies conditions and methods for identifying the best choice from a set of available options, according to a certain optimality criterion. Analyzing and solving optimization problems is an important decision support tool in modern business management, as well as in many other generally economizing activities.
Optimization is a broad area, which includes various methods and develops in numerous directions, depending on the observed class of problems. This course covers the central, classical part of optimization (i.e., optimization problems that are continuous, static, single-criterion, single-agent and deterministic), as a basis for more advanced future considerations.
The course consists of the following interrelated topics:
1. Structure and geometry of the problem (Graphical visualization of low-dimensional problems)
2. Unconstrained problem (First- and second-order optimality conditions)
3. Equality constrained problem (Lagrange multipliers method)
4. Convex problem (Numerical method of gradient descent)
5. General nonlinear problem (Karush-Kuhn-Tucker method)
6. Overview of Linear programming (Simplex method)
The course assumes prior knowledge of mathematical analysis and linear algebra. The emphasis of the course is on the application of the presented theory, through intensive training in solving practical assignments.
- Teacher: Karmela Aleksić Maslać
- Teacher: Zoran Lukić