# Milena J. PetrovićUniversity of Priština · Faculty of Science and Mathematics

Milena J. Petrović

PhD

## About

36

Publications

5,740

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213

Citations

Citations since 2017

## Publications

Publications (36)

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods...

PurposeTo ensure the correct operation of the railway vehicle, it is necessary to provide a number of supervision measures. By identifying and analyzing vibrations on the axle assemblies as well as on the floor of the box of rail vehicles, a picture of the state of the suspension and the state of the axle assemblies was obtained. This aims at early...

In this paper, we follow a chronological development of gradient descent methods and its accelerated variants later on. We specifically emphasise some contemporary approaches within this research field. Accordingly, a constructive overview over the class of hybrid accelerated models derived from the three-term hybridization process proposed by Khan...

We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence an...

In this paper we deal with a determination of numbers in a Pascal triangle that are simultaneously triangular, tetrahedral and hyper pyramidal, i.e. natural numbers n, m, k ϵ N, such that it is (n 2) = (m 3) = (k 4) for n, m, k ϵ N and n ≥ 2, m ≥ 3, k ≥ 4. The collected results, obtained by mathematical analysis, were verified by computer. For this...

We introduce a hybrid gradient model for solving unconstrained optimization problems based on one specific accelerated gradient iteration. Having applied a three term hybridization relation on transformed accelerated double step size model, we develop an efficient hybrid accelerated scheme. We determine an iterative step size variable using Backtra...

In this paper we deal with a method for the determination of numbers in a Pascal triangle that are simultaneously triangular, tetrahedral and pentaedroidni.
The collected results, obtained by mathematical analysis, were verified by computer. For this purpose, we used the C# programming language as well as the computer laboratory within our Univers...

In this paper, we deal with the dominating set and the domination number of rhomboidal cactus chains. We determine minimum dominating sets and domination numbers of two special types of rhomboidal cactus chains, meta and ortho-chains. Thereafter, we determined the minimum dominating set for the icosahedral hexagonal network.
Keywords: dominating se...

One of the main tasks in teaching mathematics is to develop students' constructive thinking. In order to effectively accomplish this task, it is necessary to make a good selection of instructional materials and teaching aids. In order to make good selection and improve the teaching of mathematics, it is, also, necessary to include a statistical ana...

E‐learning, as a complex system, includes distance learning, teaching materials in various forms and shapes, group and individual learning processes, as well as interactive and tutorial work. To increase the effectiveness and efficiency of the e‐learning system, it is necessary first of all to consider the characteristics of students and their lear...

In this paper, we are going to demonstrate a method for determining the generating functions of tetrahedral, hexahedral, octahedral, dodecahedral, and icosahedral figurative numbers. The method is based on the differences between the members of the series of the mentioned figurative numbers, as well as on the previously specified generating functio...

This paper presents a theoretical work on the study of the use of electronic textbooks (e-tutorials) as an e-learning tool. The paper reviews literature on the basic concepts of e-tutorials. The paper examines and studies previous research and findings on e-tutorials and its use in education, especially in the process of teaching and e-learning. Th...

Numerous researches in the previous period have shown the effectiveness of mathematical learning with the use of information and communication technologies (ICT) and mathematical software packages. Also, through theoretical studies and research results, the quality of mathematics teaching in schools was examined. The results of the research of the...

In recent years, there has been an increased use of information and communication technologies and mathematical software in mathematics teaching. Numerous studies of the effectiveness of mathematical learning have shown the justification and usefulness of the implementation of new teaching AIDS. They also showed that learning with educational softw...

Implementation of E-Learning is one of the ways of applying modern information technologies to achieve a high quality of higher education. The transition of higher education institutions towards E-Learning should be an integral part of strategic planning that seeks to change and improve the work of universities. This paper explains the importance o...

A hybrid accelerated model with two step length parameters for solving unconstrained optimization problems is presented. Applied hybridization process involves an efficient three term hybrid method. The accelerated double step size model is taken as guiding operator in this hybridization process. Defined method is convergent on the set of uniformly...

The aim of this paper is to set framework for the repair rate in order to achieve required availability of a repairable system with alternating renewal process where the failure rate is Weibull distributed. In order to accomplish this goal, this paper proposes a novel model for a complete stochastic analysis of the repair rate. The resulting equati...

The process of developing e-learning is based on standards in the field of information security (ISO) and learning technologies (IEEE, IMS), and criteria for quality assurance have been taken as input parameters. The overall development was carried out through the PDCA cycle and with upgraded LTSA architecture.

Vol. 17, str. 72-85, 2018 god., web lokacija gde se nalazi rad:http://um.uninp.edu.rs Tematska oblast u koju se svrstava rad: Društvene i humanističke nauke / podoblast: matematika Datum prijema rada: 01.05.2018. Apstrakt Savremena nastava matematike na svim nivoima obrazovanja uglavnom se svodi na primenu algebarskih formula i algebarskih postupak...

Vol. 17, str. 72-85, 2018 god., web lokacija gde se nalazi rad:http://um.uninp.edu.rs Tematska oblast u koju se svrstava rad: Društvene i humanističke nauke / podoblast: matematika Datum prijema rada: 01.05.2018. Apstrakt Savremena nastava matematike na svim nivoima obrazovanja uglavnom se svodi na primenu algebarskih formula i algebarskih postupak...

Apstrakt: U nastavi studenata na visokoškolskim ustanovama i studijskim programima elektronsko učenje ima značajnu ulogu. Cilj ovog istraživanja koje je sprovedeno na Alfa BK Univerzitetu u Beogradu je istražiti odnos između elektronskog učenja i unutrašnje motivacije studenata. Sveobuhvatno, rezultati ovog istraživanja potvrdili su da je elektrons...

Contemporary mathematics teaching is mostly reduced to the application of algebraic formulas and algebraic procedures. The visual-logical approach in solving mathematical tasks is very little represented in teaching mathematics. Such practice should be changed since visualization is of great importance in the process of learning and understanding m...

We analyze a performance profile of several accelerated and hybrid accelerated methods. All comparative methods are at least linearly convergent and have satisfied numerical characteristics regarding tested metrics: number of iterations, CPU time and number of function evaluations. Among the chosen set of methods we numerically show which one is th...

We present a hybridization of the accelerated gradient method with two vector directions. This hybridization is based on the usage of a chosen three term hybrid model. Derived hybrid accelerated double direction model keeps preferable properties of both
included methods. Convergence analysis demonstrates at least linear convergence of the proposed...

We present a gradient descent algorithm with a line search procedure for solving unconstrained optimization problems which is defined as a result of applying Picard-Mann hybrid iterative process on accelerated gradient descent SM method described in Stanimirović and Miladinović (Numer. Algor. 54, 503–520, 2010). Using merged features of both analyz...

We improve the convergence properties of the iterative scheme for solving unconstrained optimisation problems introduced in Petrovic et al. [‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi: 10.1007/s11075-017-0460-4 ] by optimising the value of the initial step length parameter in the backtracking line search p...

This paper presents a novel approach for estimation of repair rate in an observed system comprised of two or more components. The presented approach is based on calculation of probability density function of maximal and minimal system’s repair time by observing the repair rates of its components. Based on the obtained information it can be conclude...

Performance Based Logistics (PBL) concept has an aim to improve the system availability and it has been extensively researched in the recent years. These researches showed that inventory level does not impact system availability as much as component reliability and repair time in repairable system operating under PBL contract. Based on that, in thi...

In this paper the efficiency of accelerated gradient descent methods regarding the way of determination of accelerated factor is considered. Due to the previous researches we assert that the use of Taylor's series of posed gradient descent iteration in calculation of accelerated parameter gives better final results than some other choices. We give...

Underage costs are not easily quantifiable in spare parts management. These costs occur when a spare part is required and none are available in inventory. This paper provides another approach to underage cost optimization for subassemblies and assemblies in aviation industry. The quantity of spare parts is determined by using a method for airplane...

A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition
that relates two step lengths in the accelerated double step size gradient descent scheme.The proposed transformation is numerically
tested. Obtained results confirm the substantial progress in comparison with the sing...

This work presents a double step size algorithm with accelerated property for solving nonlinear unconstrained optimization problems. Using the inexact line search technique, as well as the approximation of the Hessian by an adequate diagonal matrix, an efficient accelerated gradient descent method is developed. The proposed method is proven to be l...

A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition
that relates two step lengths in the accelerated double step size gradient descent scheme.The proposed transformation is numerically
tested. Obtained results confirm the substantial progress in comparison with the sing...

An iterative method for solving a minimization problem of unconstrained optimization is presented. This multistep curve search method uses the specific form of iteration with two direction parameters, the approximation of Hessian by appropriately constructed diagonal matrix, and the inexact line search procedure. It is proved that constructed numer...

An iterative method for solving a minimization problem of unconstrained optimization is presented. This multistep curve search method uses the specific form of iteration with two direction parameters, the approximation of Hessian by appropriately constructed diagonal matrix, and the inexact line search procedure. It is proved that constructed numer...

Wireless communication system operating over interference limited, α-κ-μ multipath fading channel is considered. Closed form expressions for cumulative distribution function and level crossing rate of the ratio of two κ-μ random variables and the ratio of the two α-κ-μ random variables are calculated. These expressions are used for evaluation level...

## Projects

Projects (3)

Contemporary mathematics teaching is mostly reduced to the application of algebraic
formulas and algebraic procedures. The visual-logical approach in solving
mathematical tasks is very little represented in teaching mathematics. Such practice
should be changed since visualization is of great importance in the process of learning
and understanding mathematics as well as in solving mathematical tasks. This paper
suggests the possibility of developing students’ ability to perceive lawfulness among
numbers by introducing figurative numbers in mathematics teaching.

Primary goal of this project is to find new mathematical models for solving of optimized problems in wide range and their application in stochastic analysis, theory of generalized inverses and theory of fixed point. It is also, expected that the results of this project should be applied in different industrial fields.