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Papers by Milanka Filipovic Gardasevic

Research paper thumbnail of On Almost b-Metric Spaces and Related Fixed Point Results

Axioms, 2019

In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point th... more In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b-metrics to the corresponding b-metrics. Later, we show that this approach can not work for all kinds of contractions. To confirm this, we present a proof in which the contraction condition is such that it cannot be reduced to corresponding b-metrics.

Research paper thumbnail of An Algorithm For Minimization Of A Nondifferentiable Convex Function

In this paper an algorithm for minimization of a nondifferentiable function is presented. The alg... more In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yoshida regularization of the objective function and its second order Dini upper directional derivative. It is proved that the algorithm is well defined, as well as the convergence of the sequence of points generated by the algorithm to an optimal point. An estimate of the rate of convergence is given, too.

Research paper thumbnail of Nondifferentiable Convex Optimization: An Algorithm Using Moreau-Yosida Regularization

In this paper we present an algorithm for minimization of a nondifferentiable proper closed conve... more In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida regularization of the objective function we make a quadratic approximation. The purpose of the paper is to establish that the sequence of points generated by the algorithm has an accumulation point which satisfies the first order necessary and sufficient conditions. A convergence proof is given, as well as an estimate of the rate of convergence. Index Terms— Moreau-Yosida regularization, non-smooth convex optimization, second order Dini upper directional derivative.

Research paper thumbnail of Multicriteria optimization in a fuzzy environment: The fuzzy analytic hierarchy process

Yugoslav Journal of Operations Research, 2010

In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, ... more In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, and its application in solving a practical problem, are considered. The paper advocates the use of contradictory test to check the fuzzy user preferences during fuzzy AHP decision-making process. We also propose consistency check and deriving priorities from inconsistent fuzzy judgment matrices to be included in the process, in order to check if the fuzzy approach can be applied in the AHP for the problem considered. An aggregation of local priorities obtained at different levels into composite global priorities for the alternatives based on weighted-sum method is also discussed. The contradictory fuzzy judgment matrix is analyzed. Our theoretical consideration has been verified by an application of commercially available Super Decisions program (developed for solving multi-criteria optimization problems using AHP approach) on the problem previously treated in the literature. The obtaine...

Research paper thumbnail of A trust region method using subgradient for minimizing a nondifferentiable function

Yugoslav Journal of Operations Research, 2009

The minimization of a particular nondifferentiable function is considered. The first and second o... more The minimization of a particular nondifferentiable function is considered. The first and second order necessary conditions are given. A trust region method for minimization of this form of the objective function is presented. The algorithm uses the subgradient instead of the gradient. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first and second order necessary conditions.

Research paper thumbnail of Some New Observations and Results for Convex Contractions of Istratescu’s Type

Symmetry, 2019

The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric sp... more The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.

Research paper thumbnail of An algorithm using Moreau-Yosida regularization for minimization of a nondifferentiable convex function

Filomat, 2013

In this paper we present an algorithm for minimization of a nondifferentiable proper closed conve... more In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida regularization of the objective function we make a quadratic approximation. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first order necessary and sufficient conditions.

Research paper thumbnail of A New Prioritization Method in the Analytic Hierarchy Process Applied on a Case Study of the Convention Site Selection

The first part of this article is dedicated to the Analytic Hierarchy Process, particularly to th... more The first part of this article is dedicated to the Analytic Hierarchy Process, particularly to the eigenvector prioritization method. The well-known fixedpoint theorem is used for the new prioritization method which is presented in the second part of this article. Finally, using MATLAB, the numerical example, i.e., a case study of the convention site selection computed by the new prioritization method is given, and the result are pointing close a proximity to those achieved by the eigenvector prioritization method in the Super-Decision software. The result is high quality information about the factors using for the evaluating the site selection.

Research paper thumbnail of An Algorithm Using Trust Region Strategy for Minimization of a Nondifferentiable Function

Numerical Functional Analysis and Optimization, Nov 9, 2011

In this article, we present a method for minimization of a nondifferentiable function. The method... more In this article, we present a method for minimization of a nondifferentiable function. The method uses trust region strategy combined with a bundle method philosophy. It is proved that the sequence of points generated by the algorithm has an accumulation point that satisfies the first order necessary and sufficient conditions.

Research paper thumbnail of The analytic hierarchy process as a support for decision making

Spatium, 2007

The first part of this text deals with a convention site selection as one of the most lucrative a... more The first part of this text deals with a convention site selection as one of the most lucrative areas in the tourism industry. The second part gives a further description of a method for decision making - the analytic hierarchy process. The basic characteristics: hierarchy constructions and pair wise comparison on the given level of the hierarchy are allured. The third part offers an example of application. This example is solved using the Super - Decision software, which is developed as a computer support for the analytic hierarchy process. This indicates that the AHP approach is a useful tool to help support a decision of convention site selection. .

Research paper thumbnail of On an algorithm in nondifferential convex optimization

Yugoslav Journal of Operations Research, 2013

In this paper an algorithm for minimization of a nondifferentiable function is presented. The alg... more In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.

Research paper thumbnail of Numericke metode za resavanje konveksnih nediferencijabilnih optimizacionih problema

Research paper thumbnail of On Almost b-Metric Spaces and Related Fixed Point Results

Axioms, 2019

In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point th... more In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b-metrics to the corresponding b-metrics. Later, we show that this approach can not work for all kinds of contractions. To confirm this, we present a proof in which the contraction condition is such that it cannot be reduced to corresponding b-metrics.

Research paper thumbnail of An Algorithm For Minimization Of A Nondifferentiable Convex Function

In this paper an algorithm for minimization of a nondifferentiable function is presented. The alg... more In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yoshida regularization of the objective function and its second order Dini upper directional derivative. It is proved that the algorithm is well defined, as well as the convergence of the sequence of points generated by the algorithm to an optimal point. An estimate of the rate of convergence is given, too.

Research paper thumbnail of Nondifferentiable Convex Optimization: An Algorithm Using Moreau-Yosida Regularization

In this paper we present an algorithm for minimization of a nondifferentiable proper closed conve... more In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida regularization of the objective function we make a quadratic approximation. The purpose of the paper is to establish that the sequence of points generated by the algorithm has an accumulation point which satisfies the first order necessary and sufficient conditions. A convergence proof is given, as well as an estimate of the rate of convergence. Index Terms— Moreau-Yosida regularization, non-smooth convex optimization, second order Dini upper directional derivative.

Research paper thumbnail of Multicriteria optimization in a fuzzy environment: The fuzzy analytic hierarchy process

Yugoslav Journal of Operations Research, 2010

In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, ... more In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP) based on fuzzy numbers, and its application in solving a practical problem, are considered. The paper advocates the use of contradictory test to check the fuzzy user preferences during fuzzy AHP decision-making process. We also propose consistency check and deriving priorities from inconsistent fuzzy judgment matrices to be included in the process, in order to check if the fuzzy approach can be applied in the AHP for the problem considered. An aggregation of local priorities obtained at different levels into composite global priorities for the alternatives based on weighted-sum method is also discussed. The contradictory fuzzy judgment matrix is analyzed. Our theoretical consideration has been verified by an application of commercially available Super Decisions program (developed for solving multi-criteria optimization problems using AHP approach) on the problem previously treated in the literature. The obtaine...

Research paper thumbnail of A trust region method using subgradient for minimizing a nondifferentiable function

Yugoslav Journal of Operations Research, 2009

The minimization of a particular nondifferentiable function is considered. The first and second o... more The minimization of a particular nondifferentiable function is considered. The first and second order necessary conditions are given. A trust region method for minimization of this form of the objective function is presented. The algorithm uses the subgradient instead of the gradient. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first and second order necessary conditions.

Research paper thumbnail of Some New Observations and Results for Convex Contractions of Istratescu’s Type

Symmetry, 2019

The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric sp... more The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.

Research paper thumbnail of An algorithm using Moreau-Yosida regularization for minimization of a nondifferentiable convex function

Filomat, 2013

In this paper we present an algorithm for minimization of a nondifferentiable proper closed conve... more In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida regularization of the objective function we make a quadratic approximation. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first order necessary and sufficient conditions.

Research paper thumbnail of A New Prioritization Method in the Analytic Hierarchy Process Applied on a Case Study of the Convention Site Selection

The first part of this article is dedicated to the Analytic Hierarchy Process, particularly to th... more The first part of this article is dedicated to the Analytic Hierarchy Process, particularly to the eigenvector prioritization method. The well-known fixedpoint theorem is used for the new prioritization method which is presented in the second part of this article. Finally, using MATLAB, the numerical example, i.e., a case study of the convention site selection computed by the new prioritization method is given, and the result are pointing close a proximity to those achieved by the eigenvector prioritization method in the Super-Decision software. The result is high quality information about the factors using for the evaluating the site selection.

Research paper thumbnail of An Algorithm Using Trust Region Strategy for Minimization of a Nondifferentiable Function

Numerical Functional Analysis and Optimization, Nov 9, 2011

In this article, we present a method for minimization of a nondifferentiable function. The method... more In this article, we present a method for minimization of a nondifferentiable function. The method uses trust region strategy combined with a bundle method philosophy. It is proved that the sequence of points generated by the algorithm has an accumulation point that satisfies the first order necessary and sufficient conditions.

Research paper thumbnail of The analytic hierarchy process as a support for decision making

Spatium, 2007

The first part of this text deals with a convention site selection as one of the most lucrative a... more The first part of this text deals with a convention site selection as one of the most lucrative areas in the tourism industry. The second part gives a further description of a method for decision making - the analytic hierarchy process. The basic characteristics: hierarchy constructions and pair wise comparison on the given level of the hierarchy are allured. The third part offers an example of application. This example is solved using the Super - Decision software, which is developed as a computer support for the analytic hierarchy process. This indicates that the AHP approach is a useful tool to help support a decision of convention site selection. .

Research paper thumbnail of On an algorithm in nondifferential convex optimization

Yugoslav Journal of Operations Research, 2013

In this paper an algorithm for minimization of a nondifferentiable function is presented. The alg... more In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.

Research paper thumbnail of Numericke metode za resavanje konveksnih nediferencijabilnih optimizacionih problema