INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION PDF



Introduction To Nonlinear And Global Optimization Pdf

Optimization Models and Methods with Applications in Finance. Download introduction-to-nonlinear-optimization or read introduction-to-nonlinear-optimization online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get introduction-to-nonlinear-optimization book now., 3.3 Global convergence of decent algorithms The algorithms we consider are iterative descent algorithms. De nition: An algorithm A is a mapping that assigns, to each point, a.

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Introduction to Global Optimization eeci-institute.eu. Introduction to nonlinear optimization : theory, algorithms, and applications with MATLAB Responsibility Amir Beck, Technion-Israel Institute of Technology, Kfar Saba, Israel., Introduction to Global Optimization the nonlinear function that has many local minima/maxima Problem: Traditional solvers often return one of the local minima (not the global) Solution: A solver that locates globally optimal solutions Rastrigin’s Function. 6 Global Optimization Toolbox – For problems that contain multiple maxima/minima or are non-smooth Optimization T oolbox Global.

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This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state- of-the-art algorithms in global optimization. INTRODUCTION TO GLOBAL OPTIMIZATION EXPLOITING SPACE FILLING CURVES SPRINGERBRIEFS IN OPTIMIZATION Download Introduction To Global Optimization Exploiting Space Filling Curves Springerbriefs In Optimization ebook PDF or Read Online books in PDF, EPUB, and Mobi Format.

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima

nonlinear optimization, although the contributed articles mainly discuss optimization software with a local search scope. A detailed review of local and global optimization algorithms is provided by INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION By Eligius M.T. Hendrix MВґalaga University, Spain Boglarka G.-TВґ othВґ Budapest University of Technology and Economics, Hungary

Introduction to Global Optimization is the first comprehensive textbook that covers the fundamentals in global optimization. The second edition includes algorithms, applications, and complexity results for quadratic programming, concave minimization, DC and Lipshitz problems, decomposition algorithms for nonconvex optimization, and nonlinear network flow problems. Each chapter contains Introduction to Global Optimization the nonlinear function that has many local minima/maxima Problem: Traditional solvers often return one of the local minima (not the global) Solution: A solver that locates globally optimal solutions Rastrigin’s Function. 6 Global Optimization Toolbox – For problems that contain multiple maxima/minima or are non-smooth Optimization T oolbox Global

It is the hardest part of a subject called nonlinear programming (NLP). See, e Janos Pinter has an interesting online paper on Continuous Global Optimization: An Introduction to Models, Solution Approaches, Tests and Applications. A good source on information about heuristic global optimization methods for combinatorial problems is E. Aarts and J.K. Lenstra (eds.), Local Search in Structure of the course 1 Introduction and modeling 2 Unconstrained Optimization and Applications 3 Constrained Optimization and Applications 4 Optimization under

Introduction to Optimum Design, Fourth Edition, carries on the tradition of the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level in engineering departments of all disciplines, with a primary focus on mechanical, aerospace, and civil engineering Introduction to Global Optimization the nonlinear function that has many local minima/maxima Problem: Traditional solvers often return one of the local minima (not the global) Solution: A solver that locates globally optimal solutions Rastrigin’s Function. 6 Global Optimization Toolbox – For problems that contain multiple maxima/minima or are non-smooth Optimization T oolbox Global

Welcome to Global Optimization. This package provides a suite of tools for solving nonlinear optimization prob- This package provides a suite of tools for solving nonlinear optimization prob- lems, as well as a variety of other applications such as finding the … This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization …

introduction to nonlinear optimization Download introduction to nonlinear optimization or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get introduction to nonlinear optimization book now. An E cient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem y Yun-Chol Jonga a Center of Natural Sciences, University of Science, Pyongyang, DPR Korea May 3, 2012 Abstract This paper presents a practical method for nding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and man-agement. Unlike traditional methods which

Sat, 15 Dec 2018 04:09:00 GMT introduction to nonlinear optimization pdf - Introduction to non-linear optimization Ross A. Lippert D. E. Shaw Research February 25, 2008

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the

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introduction to nonlinear and global optimization pdf

Global Optimization Download eBook PDF/EPUB. XABAIKSMEFBT > eBook \\ Introduction to Nonlinear and Global Optimization Relevant PDFs [PDF] Shepherds Hey, Bfms 16: Study Score Click the web link listed below to download and read "Shepherds Hey, Bfms 16: Study Score", An E cient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem y Yun-Chol Jonga a Center of Natural Sciences, University of Science, Pyongyang, DPR Korea May 3, 2012 Abstract This paper presents a practical method for nding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and man-agement. Unlike traditional methods which.

Introduction to Nonlinear and Global Optimization CORE. - Presents various heuristic and stochastic optimization techniques demonstrating how each be applied to a variety of models from biology, engineering, finance, chemistry, and economics. This book is intended to serve as a primary text in an advanced undergraduate or graduate course focusing on nonlinear and global optimization and requires an understanding of basic calculus and linear algebra., Introduction to Global Optimization, however, is an entire textbook on constrained worldwide optimization that covers the fundamentals of the subject, presenting lots new supplies, along with algorithms, functions and complexity outcomes for quadratic programming, concave minimization, DC and Lipschitz points, and nonlinear network motion. Each chapter accommodates illustrative ….

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introduction to nonlinear and global optimization pdf

Introduction To Global Optimization Nonconvex Optimization. Most global optimization algorithms are two-phase Global phase: select a “good” starting point so that the whole search space is thoroughly and efficiently The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs..

introduction to nonlinear and global optimization pdf

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  • Keywords: nonlinear optimization, convex analysis, smooth optimization algorithms, optimality conditions, scientific computing - Hide Description This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. - Presents various heuristic and stochastic optimization techniques demonstrating how each be applied to a variety of models from biology, engineering, finance, chemistry, and economics. This book is intended to serve as a primary text in an advanced undergraduate or graduate course focusing on nonlinear and global optimization and requires an understanding of basic calculus and linear algebra.

    Global Optimization Toolbox provides functions that search for global solutions to problems that contain multiple maxima or minima. Toolbox solvers include surrogate, pattern search, genetic algorithm, particle swarm, simulated annealing, multistart, and global search. You can use these solvers for optimization problems where the objective or constraint function is continuous, discontinuous This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization … Amir Beck\Introduction to Nonlinear Optimization" Lecture Slides - Convex Optimization1 / 19 I Aconvex optimizationproblem (or just aconvex problem) is a problem consisting of minimizing a convex function over a convex set:

    Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima Sat, 15 Dec 2018 04:09:00 GMT introduction to nonlinear optimization pdf - Introduction to non-linear optimization Ross A. Lippert D. E. Shaw Research February 25, 2008

    An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and Introduction to Global Optimization the nonlinear function that has many local minima/maxima Problem: Traditional solvers often return one of the local minima (not the global) Solution: A solver that locates globally optimal solutions Rastrigin’s Function. 6 Global Optimization Toolbox – For problems that contain multiple maxima/minima or are non-smooth Optimization T oolbox Global

    nonlinear optimization, although the contributed articles mainly discuss optimization software with a local search scope. A detailed review of local and global optimization algorithms is provided by This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state

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    Chapter 16: Introduction to Nonlinear Programming A nonlinear program (NLP) is similar to a linear program in that it is composed of an objective function, general constraints, and variable bounds. optimization focus on the material, and nonlinear network flow problems are adjacent. Tags: introduction to global politics, introduction to global politics lamy, introduction to global health, introduction to global warming, introduction to global health lecture,

    INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION By Eligius M.T. Hendrix MВґalaga University, Spain Boglarka G.-TВґ othВґ Budapest University of Technology and Economics, Hungary Introduction to Global Optimization is the first comprehensive textbook that covers the fundamentals in global optimization. The second edition includes algorithms, applications, and complexity results for quadratic programming, concave minimization, DC and Lipshitz problems, decomposition algorithms for nonconvex optimization, and nonlinear network flow problems. Each chapter contains

    Over the years, many techniques were developed for finding the global minimum of a nonlinear optimization problem. These techniques include Statistical Optimization [3], Simulated Annealing [4], Genetic Algorithms [5], Particle Swarm Optimization (PSO) [6], Weed Invasive Optimization [7], Wind Optimization [8], and Ant Colony Optimization [9], just to mention a few. All of these techniques introduction to nonlinear optimization Download introduction to nonlinear optimization or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get introduction to nonlinear optimization book now.

    Introduction to Global Optimization (GO) min x 2 S R n f (x ) Гў Branch & Bound - exact techniques Гў Heuristic methods B&B requires lower bounds (e.g., convex envelopes) and upper Over the years, many techniques were developed for finding the global minimum of a nonlinear optimization problem. These techniques include Statistical Optimization [3], Simulated Annealing [4], Genetic Algorithms [5], Particle Swarm Optimization (PSO) [6], Weed Invasive Optimization [7], Wind Optimization [8], and Ant Colony Optimization [9], just to mention a few. All of these techniques

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    Introduction to Global Optimization eeci-institute.eu. global minimum when there are lots of local minima. This is why convexity is important: if S is a convex set and f is a convex function then any local minimum of f is also a global minimum., This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization ….

    A review of recent advances in global optimization and bilevel nonlinear optimization. Keywords Global optimization · NLP · MINLP · DAE · SIP · Nonfactorable models · Bilevel optimization 1 Introduction Global optimization addresses the computation and characterization of global solutions to nonconvex continuous, mixed-integer, differential-algebraic, bilevel, and non-factorable This self-contained text provides a solid Introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization …

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization … Introduction To Nonlinear And Global Optimization Author : Eligius M.T. Hendrix language : en Publisher: Springer Release Date : 2010-04-27. PDF Download Introduction To Nonlinear And Global Optimization Books For free written by Eligius M.T. Hendrix and has been published by Springer this book supported file pdf, txt, epub, kindle and other

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied Most global optimization algorithms are two-phase Global phase: select a “good” starting point so that the whole search space is thoroughly and efficiently

    Introduction to nonlinear optimization : theory, algorithms, and applications with MATLAB Responsibility Amir Beck, Technion-Israel Institute of Technology, Kfar Saba, Israel. A review of recent advances in global optimization and bilevel nonlinear optimization. Keywords Global optimization В· NLP В· MINLP В· DAE В· SIP В· Nonfactorable models В· Bilevel optimization 1 Introduction Global optimization addresses the computation and characterization of global solutions to nonconvex continuous, mixed-integer, differential-algebraic, bilevel, and non-factorable

    Welcome to Global Optimization. This package provides a suite of tools for solving nonlinear optimization prob- This package provides a suite of tools for solving nonlinear optimization prob- lems, as well as a variety of other applications such as finding the … Over the years, many techniques were developed for finding the global minimum of a nonlinear optimization problem. These techniques include Statistical Optimization [3], Simulated Annealing [4], Genetic Algorithms [5], Particle Swarm Optimization (PSO) [6], Weed Invasive Optimization [7], Wind Optimization [8], and Ant Colony Optimization [9], just to mention a few. All of these techniques

    Introduction to Optimum Design, Fourth Edition, carries on the tradition of the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level in engineering departments of all disciplines, with a primary focus on mechanical, aerospace, and civil engineering Most global optimization algorithms are two-phase Global phase: select a “good” starting point so that the whole search space is thoroughly and efficiently

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization … This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state- of-the-art algorithms in global optimization.

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    2 Global Optimization for Nonlinear Model Fitting 2.1 The Model Calibration Problem Model development is an essential research tool in many quantitative studies. 2 Global Optimization for Nonlinear Model Fitting 2.1 The Model Calibration Problem Model development is an essential research tool in many quantitative studies.

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    The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs. nonlinear optimization, although the contributed articles mainly discuss optimization software with a local search scope. A detailed review of local and global optimization algorithms is provided by

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    Over the years, many techniques were developed for finding the global minimum of a nonlinear optimization problem. These techniques include Statistical Optimization [3], Simulated Annealing [4], Genetic Algorithms [5], Particle Swarm Optimization (PSO) [6], Weed Invasive Optimization [7], Wind Optimization [8], and Ant Colony Optimization [9], just to mention a few. All of these techniques INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION By Eligius M.T. Hendrix MВґalaga University, Spain Boglarka G.-TВґ othВґ Budapest University of Technology and Economics, Hungary

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    Over the years, many techniques were developed for finding the global minimum of a nonlinear optimization problem. These techniques include Statistical Optimization [3], Simulated Annealing [4], Genetic Algorithms [5], Particle Swarm Optimization (PSO) [6], Weed Invasive Optimization [7], Wind Optimization [8], and Ant Colony Optimization [9], just to mention a few. All of these techniques An E cient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem y Yun-Chol Jonga a Center of Natural Sciences, University of Science, Pyongyang, DPR Korea May 3, 2012 Abstract This paper presents a practical method for nding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and man-agement. Unlike traditional methods which

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    INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION By Eligius M.T. Hendrix MВґalaga University, Spain Boglarka G.-TВґ othВґ Budapest University of Technology and Economics, Hungary This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization

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    (PDF) Introduction to global optimization ResearchGate. This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization … Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima.

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  • Functions . that occur in nonlinear constraints are stored in a single so-called expression graph, which is a directed acyclic graph that has variables and constants as sources and the functions . as sinks, see also [82 H. Schichl and A. Neumaier, Interval analysis on directed acyclic graphs for global optimization, J. Global Optim. 33 (2005), pp. 541 – 562. Introduction to Global Optimization Exploiting Space-Filling Curves presents an abstract of classical and new outcomes pertaining to the utilization of space-filling curves in worldwide optimization.

    Introduction to nonlinear optimization : theory, algorithms, and applications with MATLAB Responsibility Amir Beck, Technion-Israel Institute of Technology, Kfar Saba, Israel. 4 Optimization Viewpoints Mathematician - characterization of theoretical properties of optimization, convergence, existence, local convergence rates.

    nonlinear optimization, although the contributed articles mainly discuss optimization software with a local search scope. A detailed review of local and global optimization algorithms is provided by

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the

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    introduction to global optimization nonconvex optimization and its applications Sat, 29 Dec 2018 03:17:00 GMT introduction to global optimization nonconvex pdf - In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of Global Optimization Toolbox provides functions that search for global solutions to problems that contain multiple maxima or minima. Toolbox solvers include surrogate, pattern search, genetic algorithm, particle swarm, simulated annealing, multistart, and global search. You can use these solvers for optimization problems where the objective or constraint function is continuous, discontinuous

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    Welcome to Global Optimization. This package provides a suite of tools for solving nonlinear optimization prob- This package provides a suite of tools for solving nonlinear optimization prob- lems, as well as a variety of other applications such as finding the … Welcome to Global Optimization. This package provides a suite of tools for solving nonlinear optimization prob- This package provides a suite of tools for solving nonlinear optimization prob- lems, as well as a variety of other applications such as finding the …

    - Presents various heuristic and stochastic optimization techniques demonstrating how each be applied to a variety of models from biology, engineering, finance, chemistry, and economics. This book is intended to serve as a primary text in an advanced undergraduate or graduate course focusing on nonlinear and global optimization and requires an understanding of basic calculus and linear algebra. Similar situation in Bertsekas, Nonlinear Programming (1999): 777 pages, but only the definition of global minima and maxima is given! Nocedal & Wrigth, “Numerical Optimization”, 2nd edition, 2006:

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    4 Optimization Viewpoints Mathematician - characterization of theoretical properties of optimization, convergence, existence, local convergence rates. 2 Ruth Misener, Christodoulos A. Floudas 1 Introduction Deterministic global optimization of mixed-integer nonlinear programs (MINLP) is broadly

    introduction to nonlinear optimization Download introduction to nonlinear optimization or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get introduction to nonlinear optimization book now. Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria.

    lectures on global optimization Download lectures on global optimization or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get lectures on global optimization book now. This site is like a library, Use search box in … A review of recent advances in global optimization and bilevel nonlinear optimization. Keywords Global optimization · NLP · MINLP · DAE · SIP · Nonfactorable models · Bilevel optimization 1 Introduction Global optimization addresses the computation and characterization of global solutions to nonconvex continuous, mixed-integer, differential-algebraic, bilevel, and non-factorable

    nonlinear optimization, although the contributed articles mainly discuss optimization software with a local search scope. A detailed review of local and global optimization algorithms is provided by Download introduction-to-nonlinear-optimization or read introduction-to-nonlinear-optimization online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get introduction-to-nonlinear-optimization book now.

    3.3 Global convergence of decent algorithms The algorithms we consider are iterative descent algorithms. De nition: An algorithm A is a mapping that assigns, to each point, a An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and

    2 Global Optimization for Nonlinear Model Fitting 2.1 The Model Calibration Problem Model development is an essential research tool in many quantitative studies. Functions . that occur in nonlinear constraints are stored in a single so-called expression graph, which is a directed acyclic graph that has variables and constants as sources and the functions . as sinks, see also [82 H. Schichl and A. Neumaier, Interval analysis on directed acyclic graphs for global optimization, J. Global Optim. 33 (2005), pp. 541 – 562.

    This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state Introduction to Global Optimization (GO) min x 2 S R n f (x ) Гў Branch & Bound - exact techniques Гў Heuristic methods B&B requires lower bounds (e.g., convex envelopes) and upper

    12 Gradient descent (conceptual description) Idea: 1) Make a guess 2) Compute the derivative at this point (i.e. the slope) 3) Follow the direction of the slope (i.e. descend) Introduction to Global Optimization (GO) min x 2 S R n f (x ) Гў Branch & Bound - exact techniques Гў Heuristic methods B&B requires lower bounds (e.g., convex envelopes) and upper

    An E cient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem y Yun-Chol Jonga a Center of Natural Sciences, University of Science, Pyongyang, DPR Korea May 3, 2012 Abstract This paper presents a practical method for nding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and man-agement. Unlike traditional methods which This paper is a mini-course about global optimization techniques in nonconvex programming; it deals with some theoretical aspects of nonlinear programming as well as with some of the current state

    global minimum when there are lots of local minima. This is why convexity is important: if S is a convex set and f is a convex function then any local minimum of f is also a global minimum. Chapter 16: Introduction to Nonlinear Programming A nonlinear program (NLP) is similar to a linear program in that it is composed of an objective function, general constraints, and variable bounds.

    Chapter 16: Introduction to Nonlinear Programming A nonlinear program (NLP) is similar to a linear program in that it is composed of an objective function, general constraints, and variable bounds. This self-contained text provides a solid Introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization …

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    An E cient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem y Yun-Chol Jonga a Center of Natural Sciences, University of Science, Pyongyang, DPR Korea May 3, 2012 Abstract This paper presents a practical method for nding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and man-agement. Unlike traditional methods which INTRODUCTION TO NONLINEAR AND GLOBAL OPTIMIZATION By Eligius M.T. Hendrix MВґalaga University, Spain Boglarka G.-TВґ othВґ Budapest University of Technology and Economics, Hungary