Bi Level Strategies In Semi Infinite Programming

Author : Oliver Stein
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 55,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781441991645

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Bi-Level Strategies in Semi-Infinite Programming by Oliver Stein Pdf

Semi-infinite optimization is a vivid field of active research. Recently semi infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

Author : Jacek Leskow,Martin Puchet,Lionello F. Punzo
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 54,8 Mb
Release : 2006-05-06
Category : Business & Economics
ISBN : 9783540284444

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New Tools of Economic Dynamics by Jacek Leskow,Martin Puchet,Lionello F. Punzo Pdf

New Tools of Economic Dynamics gives an introduction and overview of recently developed methods and tools, most of them developed outside economics, to deal with the qualitative analysis of economic dynamics. It reports the results of a three-year research project by a European and Latin American network on the intersection of economics with mathematical, statistical, and computational methods and techniques. Focusing upon the evolution and manifold structure of complex dynamic phenomena, the book reviews and shows applications of a variety of tools, such as symbolic and coded dynamics, interacting agents models, microsimulation in econometrics, large-scale system analysis, and dynamical systems theory. It shows the potential of a comprehensive analysis of growth, fluctuations, and structural change along the lines indicated by pioneers like Harrod, Haavelmo, Hicks, Goodwin, Morishima, and it highlights the explanatory power of the qualitative approach they initiated.

Author : Helmut Neunzert,Dieter Prätzel-Wolters
Publisher : Springer
Page : 437 pages
File Size : 55,7 Mb
Release : 2015-11-01
Category : Mathematics
ISBN : 9783662482582

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Currents in Industrial Mathematics by Helmut Neunzert,Dieter Prätzel-Wolters Pdf

This book offers an insider's view of how industrial problems are translated into mathematics and how solving the mathematics leads to convincing industrial solutions as well. In 6 technical chapters, a wide range of industrial problems is modeled, simulated, and optimized; 4 others describe the modeling, computing, optimization, and data analysis concepts shaping the work of the Fraunhofer ITWM. Each technical chapter illustrates how the relevant mathematics has been adapted or extended for the specific application and details the underlying practical problem and resulting software. The final chapter shows how the use of mathematical modeling in the classroom can change the image of this subject, making it exciting and fun.

Author : Rembert Reemtsen,Jan-J. Rückmann
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 41,9 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475728682

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Semi-Infinite Programming by Rembert Reemtsen,Jan-J. Rückmann Pdf

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming. SIP problems include finitely many variables and, in contrast to finite optimization problems, infinitely many inequality constraints. Prob lems of this type naturally arise in approximation theory, optimal control, and at numerous engineering applications where the model contains at least one inequality constraint for each value of a parameter and the parameter, repre senting time, space, frequency etc., varies in a given domain. The treatment of such problems requires particular theoretical and numerical techniques. The theory in SIP as well as the number of numerical SIP methods and appli cations have expanded very fast during the last years. Therefore, the main goal of this monograph is to provide a collection of tutorial and survey type articles which represent a substantial part of the contemporary body of knowledge in SIP. We are glad that leading researchers have contributed to this volume and that their articles are covering a wide range of important topics in this subject. It is our hope that both experienced students and scientists will be well advised to consult this volume. We got the idea for this volume when we were organizing the semi-infinite pro gramming workshop which was held in Cottbus, Germany, in September 1996.

Author : Stephan Dempe,Alain Zemkoho
Publisher : Springer Nature
Page : 679 pages
File Size : 54,9 Mb
Release : 2020-11-23
Category : Business & Economics
ISBN : 9783030521196

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Bilevel Optimization by Stephan Dempe,Alain Zemkoho Pdf

2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.

Author : Guangquan Zhang,Jie Lu,Ya Gao
Publisher : Springer
Page : 385 pages
File Size : 40,6 Mb
Release : 2015-02-07
Category : Technology & Engineering
ISBN : 9783662460597

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Multi-Level Decision Making by Guangquan Zhang,Jie Lu,Ya Gao Pdf

This monograph presents new developments in multi-level decision-making theory, technique and method in both modeling and solution issues. It especially presents how a decision support system can support managers in reaching a solution to a multi-level decision problem in practice. This monograph combines decision theories, methods, algorithms and applications effectively. It discusses in detail the models and solution algorithms of each issue of bi-level and tri-level decision-making, such as multi-leaders, multi-followers, multi-objectives, rule-set-based, and fuzzy parameters. Potential readers include organizational managers and practicing professionals, who can use the methods and software provided to solve their real decision problems; PhD students and researchers in the areas of bi-level and multi-level decision-making and decision support systems; students at an advanced undergraduate, master’s level in information systems, business administration, or the application of computer science.

Author : Stephan Dempe,Vyacheslav Kalashnikov
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 55,9 Mb
Release : 2006-09-19
Category : Mathematics
ISBN : 9780387342214

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Optimization with Multivalued Mappings by Stephan Dempe,Vyacheslav Kalashnikov Pdf

This book focuses on the tremendous development that has taken place recently in the field of of nondifferentiable nonconvex optimization. Coverage includes the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the co-derivative of Mordukhovich), the opening of new applications (the calibration of water supply systems), and the elaboration of new solution algorithms (e.g., smoothing methods).

Author : Miguel Ángel Goberna,Marco A. López
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 45,6 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9781475734034

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Semi-Infinite Programming by Miguel Ángel Goberna,Marco A. López Pdf

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite. This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields. The volume is divided into four parts. Part I reviews the first decade of SIP (1962-1972). Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming. New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III. Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 47,6 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Author : Honglei Xu,Kok Lay Teo,Yi Zhang
Publisher : Springer
Page : 269 pages
File Size : 41,7 Mb
Release : 2014-06-26
Category : Mathematics
ISBN : 9783662434048

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Optimization and Control Techniques and Applications by Honglei Xu,Kok Lay Teo,Yi Zhang Pdf

This book presents advances in state-of-the-art solution methods and their applications to real life practical problems in optimization, control and operations research. Contributions from world-class experts in the field are collated here in two parts, dealing first with optimization and control theory and then with techniques and applications. Topics covered in the first part include control theory on infinite dimensional Banach spaces, history-dependent inclusion and linear programming complexity theory. Chapters also explore the use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems and look at multi-objective semi-infinite optimization problems and production planning problems. In the second part, the authors address techniques and applications of optimization and control in a variety of disciplines, such as chaos synchronization, facial expression recognition and dynamic input-output economic models. Other applications considered here include image retrieval, natural earth satellites orbital transfers, snap-back repellers and modern logistic systems. Readers will learn of advances in optimization, control and operations research, as well as potential new avenues of research and development. The book will appeal to scientific researchers, mathematicians and all specialists interested in the latest advances in optimization and control.

Author : Society for Industrial and Applied Mathematics
Publisher : Unknown
Page : 784 pages
File Size : 51,7 Mb
Release : 2004
Category : Control theory
ISBN : UCSD:31822022876429

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SIAM Journal on Control and Optimization by Society for Industrial and Applied Mathematics Pdf

Author : Jonathan F. Bard
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 45,8 Mb
Release : 1998-12-31
Category : Business & Economics
ISBN : 0792354583

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Practical Bilevel Optimization by Jonathan F. Bard Pdf

The focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology. What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field. Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists.

Author : Surapati Pramanik,Partha Pratim Dey
Publisher : Infinite Study
Page : 12 pages
File Size : 44,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX

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Bi-level Linear Programming Problem with Neutrosophic Numbers by Surapati Pramanik,Partha Pratim Dey Pdf

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy.

Author : Stephan Dempe
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 54,5 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9780306480454

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Foundations of Bilevel Programming by Stephan Dempe Pdf

Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.

Author : A. V. Fiacco,K. O. Kortanek
Publisher : Unknown
Page : 340 pages
File Size : 43,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3642464785

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Semi-Infinite Programming and Applications by A. V. Fiacco,K. O. Kortanek Pdf