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Bilevel Programming Problems

Bilevel Programming Problems PDF Author: Stephan Dempe
Publisher: Springer
ISBN: 3662458276
Category : Business & Economics
Languages : en
Pages : 325

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Book Description
This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

Bilevel Programming Problems

Bilevel Programming Problems PDF Author: Stephan Dempe
Publisher: Springer
ISBN: 3662458276
Category : Business & Economics
Languages : en
Pages : 325

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Book Description
This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC

Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC PDF Author: Didier Aussel
Publisher: Springer
ISBN: 981104774X
Category : Mathematics
Languages : en
Pages : 124

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Book Description
The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.

Bi-level Linear Programming Problem with Neutrosophic Numbers

Bi-level Linear Programming Problem with Neutrosophic Numbers PDF Author: Surapati Pramanik
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12

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Book Description
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.

Foundations of Bilevel Programming

Foundations of Bilevel Programming PDF Author: Stephan Dempe
Publisher: Springer Science & Business Media
ISBN: 030648045X
Category : Mathematics
Languages : en
Pages : 309

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Book Description
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.

Bilevel Optimization

Bilevel Optimization PDF Author: Stephan Dempe
Publisher: Springer Nature
ISBN: 3030521192
Category : Business & Economics
Languages : en
Pages : 672

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Book Description
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.

Practical Bilevel Optimization

Practical Bilevel Optimization PDF Author: Jonathan F. Bard
Publisher: Springer Science & Business Media
ISBN: 1475728360
Category : Business & Economics
Languages : en
Pages : 476

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Book Description
The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problern in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential 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.

Advances in Mathematics Research

Advances in Mathematics Research PDF Author: Gabriel Oyibo
Publisher: Nova Publishers
ISBN: 9781590332238
Category : Mathematics
Languages : en
Pages : 244

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Book Description
This book presents research from leading scholars throughout the world. Contents: Preface; Reduction Theory of Von Neumann Algebras in Real Case; Some Recent Results and Problems for Set-Valued Mappings; On (p, s)-Regularity of the Inversion Problem for the Sturm-Liouville Equation; Spaces of Functions Holomorphic in Convex Bounded Domains of C and Smooth Up to the Boundary; Weak Bilevel Programming Problems: Existence of Solutions; A Remark about the Shannon's Sampling Theorem; Quantum Integral Equations with Kernels of Quantum White Noise in Space and Time; On the Dependence Structure of a System of Components with a Multivariate Shot-Noise Hazard Rate Process; Global Exponential Stability and Periodic Solutions of Cellular Neural Networks (CNN's) with Delays; Some Remarks on the Charged Top; On a Transport Operator Arising in Growing Cell Populations Spectral Analysis; On Viscoelastic Fluids in Elongation; Fuzzy relational Model for Knowledge Processing and Decision Making; Index

Solving Optimization Problems with MATLAB®

Solving Optimization Problems with MATLAB® PDF Author: Dingyü Xue
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110663694
Category : Computers
Languages : en
Pages : 342

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Book Description
This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided.

An Algorithm for Solving a Class of Bilevel Programming Problems

An Algorithm for Solving a Class of Bilevel Programming Problems PDF Author: Stephan Dempe
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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Book Description


Multi-level linear programming problem with neutrosophic numbers: A goal programming strategy

Multi-level linear programming problem with neutrosophic numbers: A goal programming strategy PDF Author: Surapati Pramanik
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 13

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Book Description
In the paper, we propose an alternative strategy for multi-level linear programming (MLP) problem with neutrosophic numbers through goal programming strategy. Multi-level linear programming problem consists of k levels where there is an upper level at the first level and multiple lower levels at the second level with one objective function at every level.