Methods of numerical optimization | Faculty of Technical Sciences

Subject: Methods of numerical optimization (17.0M532)

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 2, Semester: Winter)
Master Academic Studies	Information Engineering (Year: 1, Semester: Winter)

General information:

Category	Professional-applicative
Scientific or art field	Teorijska i primenjena matematika
ECTS	4

Acquisition of basic knowledge in numerical optimization. Developing ability for independent analysis and solving of various optimization problems. Student is trained for independent creation of numerical models of optimization problems.

Basic knowledge in theory of numerical optimization. Enable students to develop and analyze numerical models.

Mathematical formulation of the optimization problem. Rate of convergence. Global and local optimization. Constrained and unconstrained optimization. Stochastic and deterministic optimization. Continuous and discrete optimization. Line search methods: Wolf conditions, Steepest descent method, Newton's method, Quasi-Newton methods. Trust-region methods. Cauchy point. Conjugate Gradient (CG) methods: linear CG method, nonlinear CG method. Least-squares (LS) problems: linear LS problems, nonlinear LS problems, Gauss-Newton method. Introduction to constrained optimization. Penalty function. Quadratic programming.

Lectures and practical exercises on the computer. During lectures theoretical part of the course is presented and followed by typical examples from optimization theory. During practice, which accompanies lectures, typical problems are solved applying certain computer software.

Authors	Title	Year	Publisher	Language
Nocedal, J., Wright, S.	Numerical Optimization	2006	Springer, New York	English
Carnahan, B., Luther, H.A., Wilkes, J.O.	Applied Numerical Methods	1969	John Wiley & Sons, Inc., New York	English
Snyman, J.A.	Practical Mathematical Optimization : An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms	2005	Springer-Verlag, New York	English
Horst, R., Hoang, T.	Global Optimization : Deterministic Approaches	1996	Springer Verlag, Berlin	English