Numerical optimization | Faculty of Technical Sciences

Subject: Numerical optimization (17.IA022)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Engineering Animation (Year: 1, Semester: Winter)

General information:

Category	Theoretical-methodological
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. Special attention is dedicated to optimization problems in the filed of digital image processing.

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, Levenberg-Marquardt 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. Special attention is dedicated to optimization problems in the filed of digital image processing.

Authors	Title	Year	Publisher	Language
Horst, R., Hoang, T.	Global Optimization : Deterministic Approaches	1996	Springer Verlag, Berlin	English
Nocedal, J., Wright, S.	Numerical Optimization	2006	Springer, 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