Characterization Of Proper Optimal Elements With Variable Ordering Structures

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Characterization of Proper Optimal Elements with Variable Ordering Structures

Author : Gabriele Eichfelder
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (935 download)

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Book Synopsis Characterization of Proper Optimal Elements with Variable Ordering Structures by : Gabriele Eichfelder

Download or read book Characterization of Proper Optimal Elements with Variable Ordering Structures written by Gabriele Eichfelder and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. As these vector optimization problems are not only of interest in applications but also mathematical challenging, in recent publications it was started to develop a comprehensive theory. In doing that also notions of proper efficiency where generalized to variable ordering structures. In this paper we study the relations between several types of proper optimality notions, among others based on local and global approximations of the considered sets. We give scalarization results based on new functionals defined by elements from the dual cones which allow characterizations also in the nonconvex case.

Variable Ordering Structures in Vector Optimization

Author : Gabriele Eichfelder
Publisher : Springer Science & Business Media
ISBN 13 : 3642542832
Total Pages : 330 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Variable Ordering Structures in Vector Optimization by : Gabriele Eichfelder

Download or read book Variable Ordering Structures in Vector Optimization written by Gabriele Eichfelder and published by Springer Science & Business Media. This book was released on 2014-04-04 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.

Properly Optimal Elements in Vector Optimization with Variable Ordering Structures

Author : Gabriele Eichfelder
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (935 download)

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Book Synopsis Properly Optimal Elements in Vector Optimization with Variable Ordering Structures by : Gabriele Eichfelder

Download or read book Properly Optimal Elements in Vector Optimization with Variable Ordering Structures written by Gabriele Eichfelder and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.

Variational Analysis and Set Optimization

Author : Akhtar A. Khan
Publisher : CRC Press
ISBN 13 : 1351712071
Total Pages : 324 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Variational Analysis and Set Optimization by : Akhtar A. Khan

Download or read book Variational Analysis and Set Optimization written by Akhtar A. Khan and published by CRC Press. This book was released on 2019-06-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.

Applications of Nonlinear Analysis

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 3319898159
Total Pages : 932 pages
Book Rating : 4.3/5 (198 download)

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Book Synopsis Applications of Nonlinear Analysis by : Themistocles M. Rassias

Download or read book Applications of Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-29 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.

Combinatorial Optimization and Applications

Author : Weili Wu
Publisher : Springer Nature
ISBN 13 : 3031496116
Total Pages : 535 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Combinatorial Optimization and Applications by : Weili Wu

Download or read book Combinatorial Optimization and Applications written by Weili Wu and published by Springer Nature. This book was released on 2024-01-09 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 14461 and LNCS 14462 constitutes the refereed proceedings of the 17th International Conference on Combinatorial Optimization and Applications, COCOA 2023, held in Hawaii, HI, USA, during December 15–17, 2023. The 73 full papers included in the proceedings were carefully reviewed and selected from 117 submissions. They were organized in topical sections as follows: Part I: Optimization in graphs; scheduling; set-related optimization; applied optimization and algorithm; Graph planer and others; Part II: Modeling and algorithms; complexity and approximation; combinatorics and computing; optimization and algorithms; extreme graph and others; machine learning, blockchain and others.

Modelling, Computation and Optimization in Information Systems and Management Sciences

Author : Hoai An Le Thi
Publisher : Springer
ISBN 13 : 3319181610
Total Pages : 521 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Modelling, Computation and Optimization in Information Systems and Management Sciences by : Hoai An Le Thi

Download or read book Modelling, Computation and Optimization in Information Systems and Management Sciences written by Hoai An Le Thi and published by Springer. This book was released on 2015-05-04 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings set contains 85 selected full papers presented at the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO 2015, held on May 11–13, 2015 at Lorraine University, France. The present part I of the 2 volume set includes articles devoted to Combinatorial optimization and applications, DC programming and DCA: thirty years of Developments, Dynamic Optimization, Modelling and Optimization in financial engineering, Multiobjective programming, Numerical Optimization, Spline Approximation and Optimization, as well as Variational Principles and Applications.

Variational Analysis and Applications

Author : Boris S. Mordukhovich
Publisher : Springer
ISBN 13 : 3319927752
Total Pages : 636 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Variational Analysis and Applications by : Boris S. Mordukhovich

Download or read book Variational Analysis and Applications written by Boris S. Mordukhovich and published by Springer. This book was released on 2018-08-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.

Recent Developments in Vector Optimization

Author : Qamrul Hasan Ansari
Publisher : Springer Science & Business Media
ISBN 13 : 3642211143
Total Pages : 568 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Recent Developments in Vector Optimization by : Qamrul Hasan Ansari

Download or read book Recent Developments in Vector Optimization written by Qamrul Hasan Ansari and published by Springer Science & Business Media. This book was released on 2011-09-21 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

Multiple Criteria Decision Analysis

Author : Salvatore Greco
Publisher : Springer
ISBN 13 : 149393094X
Total Pages : 1356 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Multiple Criteria Decision Analysis by : Salvatore Greco

Download or read book Multiple Criteria Decision Analysis written by Salvatore Greco and published by Springer. This book was released on 2016-02-18 with total page 1356 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.

Structural Sensitivity Analysis and Optimization 1

Author : Kyung K. Choi
Publisher : Springer Science & Business Media
ISBN 13 : 0387271694
Total Pages : 457 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Structural Sensitivity Analysis and Optimization 1 by : Kyung K. Choi

Download or read book Structural Sensitivity Analysis and Optimization 1 written by Kyung K. Choi and published by Springer Science & Business Media. This book was released on 2006-12-30 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Structural Sensitivity Analysis and Optimization 2

Author : K. K. Choi
Publisher : Springer Science & Business Media
ISBN 13 : 0387273069
Total Pages : 336 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Structural Sensitivity Analysis and Optimization 2 by : K. K. Choi

Download or read book Structural Sensitivity Analysis and Optimization 2 written by K. K. Choi and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1993 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set-valued Optimization

Author : Akhtar A. Khan
Publisher : Springer
ISBN 13 : 3642542654
Total Pages : 781 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Set-valued Optimization by : Akhtar A. Khan

Download or read book Set-valued Optimization written by Akhtar A. Khan and published by Springer. This book was released on 2014-10-20 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges

Author : Nigel Powers
Publisher : CRC Press
ISBN 13 : 1351745964
Total Pages : 5447 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges by : Nigel Powers

Download or read book Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges written by Nigel Powers and published by CRC Press. This book was released on 2018-07-04 with total page 5447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges contains lectures and papers presented at the Ninth International Conference on Bridge Maintenance, Safety and Management (IABMAS 2018), held in Melbourne, Australia, 9-13 July 2018. This volume consists of a book of extended abstracts and a USB card containing the full papers of 393 contributions presented at IABMAS 2018, including the T.Y. Lin Lecture, 10 Keynote Lectures, and 382 technical papers from 40 countries. The contributions presented at IABMAS 2018 deal with the state of the art as well as emerging concepts and innovative applications related to the main aspects of bridge maintenance, safety, risk, management and life-cycle performance. Major topics include: new design methods, bridge codes, heavy vehicle and load models, bridge management systems, prediction of future traffic models, service life prediction, residual service life, sustainability and life-cycle assessments, maintenance strategies, bridge diagnostics, health monitoring, non-destructive testing, field testing, safety and serviceability, assessment and evaluation, damage identification, deterioration modelling, repair and retrofitting strategies, bridge reliability, fatigue and corrosion, extreme loads, advanced experimental simulations, and advanced computer simulations, among others. This volume provides both an up-to-date overview of the field of bridge engineering and significant contributions to the process of more rational decision-making on bridge maintenance, safety, risk, management and life-cycle performance of bridges for the purpose of enhancing the welfare of society. The Editors hope that these Proceedings will serve as a valuable reference to all concerned with bridge structure and infrastructure systems, including students, researchers and engineers from all areas of bridge engineering.

Analysis and Optimization of Prismatic and Axisymmetric Shell Structures

Author : Ernest Hinton
Publisher : Springer Science & Business Media
ISBN 13 : 0857294245
Total Pages : 519 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Analysis and Optimization of Prismatic and Axisymmetric Shell Structures by : Ernest Hinton

Download or read book Analysis and Optimization of Prismatic and Axisymmetric Shell Structures written by Ernest Hinton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shell-type structures can be found almost everywhere. They appear in natural forms but also as man-made, load-bearing components in diverse engineering systems. Mankind has struggled to replicate nature’s optimization of such structures but using modern computational tools it is now possible to analyse, design and optimise them systematically. Analysis and Optimization of Prismatic and Axisymmetric Shell Structures features: comprehensive coverage of the background theory of shell structures; development and implementation of reliable, creative and efficient computational tools for static and free-vibration analysis and structural optimization of variable-thickness shells and folded-plate structures; integrated computer-aided curve and surface modelling tools and automatic mesh generation, structural analysis sensitivity analysis and mathematical programming methods; well-documented, downloadable Fortran software for these techniques using finite element and finite strip simulations which can be readily adapted by the reader for the solution of practical problems or for use within a teaching or research environment. Written by leading experts in finite element and finite strip methods, Analysis and Optimization of Prismatic and Axisymmetric Shell Structures will be of great interest to researchers in structural mechanics and in automotive, aerospace and civil engineering as well as to designers from all fields using shell structures for their strength-per-unit-mass advantages.