Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Nonlinear programming (17.0M527)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Information Engineering (Godina: 1, Summer)
Master Academic Studies	Mathematics in Engineering (Godina: 1, Summer)
Master Academic Studies	Information and Analytics Engineering (Godina: 1, Summer)

General information:

Category	Theoretical-methodological
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	5

Educational goal:

Enabling students to develop abstract thinking and acquire knowledge about the theory of nonlinear programming. The goals of the course are to develop a way of thinking in the students, that will enable constructing a mathematical model for the optimization problems stemming from applications, and to successfully solve such models. The majority of the problems are expected to be non-linear and of diverse nature. Thus, to successfully solve them, the student is trained to use the appropriate software (matlab, Mathematica).

Educational outcome:

To use the acquired knowledge in further education and in practice, postulate and solve mathematical models in engineering subjects using the knowledge about nonlinear programming. The models usually originate from applications and multidisciplinary knowledge is required for solving them successfully.

Course content:

Theoretical teaching (lectures): Introduction (convex sets, convex functions). Classic optimization methods (method of elimination of variables, Lagrange multiplier method, Courant method). One-dimensional optimization (Fibonacci method, golden section method; Newton's method; cut-method; polynomial approximation method). Unconditional optimization without calculation of derivatives (Hooke-Jeeves's method; Powell's method) unconditional optimization for differential functions (Cauchy's method of the sharpest decay; modification of Cauchy's method; Newton's method; methods of variable metric). Convex programming (convex programs, Kuhn-Tucker theorems, linear constrained programs, dual problems). Practical classes (exercises): The exercises work on appropriate examples from theoretical instruction that trains the given material and, therefore, the exercises contribute to the understanding of the given material.

Teaching methods:

Lectures. Numerical calculation classes. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. During the practice classes which follow the lectures, the subject matter is supported by characteristic examples to provide further practice and better understanding In addition to lectures and practice classes there are regular consultations. The students can take partial exams during the course.

Literature:

Authors	Title	Year	Publisher	Language
Ralević, N.	Odabrana poglavlja iz matematike	2010	Symbol, Novi Sad	Serbian language
Petrić, J., Zlobec, S.	Nelinearno programiranje	1989	Naučna knjiga, Beograd	Serbian language
Nocedal, J., Wright, S.	Numerical Optimization	2006	Springer, New York	English
Bazaraa, M.S., Shetty, C.M.	Nonlinear programming : theory and algorithms	1979	John Wiley and Sons, New York	English
Martić, Lj.	Nelinearno programiranje	1973	Informator, Zagreb	Serbian language
Petrić, J.	Operaciona istraživanja	1987	Naučna knjiga, Beograd	Serbian language

Knowledge evaluation:

Course activity	Pre-examination	Obligations	Number of points
Test	Yes	Yes	10.00
Project	Yes	Yes	15.00
Exercise attendance	Yes	Yes	2.00
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Final exam - part two	No	No	25.00
Lecture attendance	Yes	Yes	3.00
Final exam - part one	No	No	25.00
Written part of the exam - tasks and theory	No	Yes	50.00