Bücher der Reihe Springer Optimization and Its Applications

In this book, theory of large scale optimization is introduced with case studies of real-world problems and applications of structured mathematical modeling. The large scale optimization methods are represented by various theories such as Benders¿ decomposition, logic-based Benders¿ decomposition, Lagrangian relaxation, Dantzig ¿Wolfe decomposition, multi-tree decomposition, Van Roy¿ cross decomposition and parallel decomposition for mathematical programs such as mixed integer nonlinear programming and stochastic programming. Case studies of large scale optimization in supply chain management, smart manufacturing, and Industry 4.0 are investigated with efficient implementation for real-time solutions. The features of case studies cover a wide range of fields including the Internet of things, advanced transportation systems, energy management, supply chain networks, service systems, operations management, risk management, and financial and sales management. Instructors, graduate students, researchers, and practitioners, would benefit from this book finding the applicability of large scale optimization in asynchronous parallel optimization, real-time distributed network, and optimizing the knowledge-based expert system for convex and non-convex problems.

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

The contributions in this book focus an approach to facility location theory through game theoretical tools highlighting situations where a location decision is faced by several decision makers and leading to a game theoretical framework in non-cooperative and cooperative methods.

This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable.The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokolowski and Antoni Zochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.

This book focuses on recent research in modern optimization and its implications in control and data analysis.

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields.

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory.

This book presents a selection of advanced case studies that cover a substantial range of issues and real-world challenges and applications in space engineering. Vital mathematical modeling, optimization methodologies and numerical solution aspects of each application case study are presented in detail, with discussions of a range of advanced model development and solution techniques and tools.Space engineering challenges are discussed in the following contexts: .Advanced Space Vehicle Design.Computation of Optimal Low Thrust Transfers.Indirect Optimization of Spacecraft Trajectories.Resource-Constrained Scheduling,.Packing Problems in Space.Design of Complex Interplanetary Trajectories.Satellite Constellation Image Acquisition.Re-entry Test Vehicle Configuration Selection.Collision Risk Assessment on Perturbed Orbits.Optimal Robust Design of Hybrid Rocket Engines.Nonlinear Regression Analysis in Space Engineering.Regression-Based Sensitivity Analysis and Robust Design.Low-Thrust Multi-Revolution Orbit Transfers.Modeling and Optimization of Balance Layout Problems.Pilot-Induced Oscillations Alleviation.Modeling and Optimization of Hybrid Transfers to Near-Earth Objects.Probabilistic Safety Analysis of the Collision Between Space Debris and Satellite.Flatness-based Low-thrust Trajectory Optimization for Spacecraft Proximity Operations The contributing authors are expert researchers and practitioners in either the space engineering and/or in the applied optimization fields. Researchers and practitioners working in various applied aspects of space engineering will find this book practical and informative. Academics, graduate and post-graduate students in aerospace engineering, applied mathematics, operations research, optimization, and optimal control, will find this book useful.

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies.

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering.Key topics covered in this book include:Quasi meansApproximate isometriesFunctional equations in hypergroupsStability of functional equationsFischer-Muszély equationHaar meager sets and Haar null setsDynamical systemsFunctional equations in probability theoryStochastic convex orderingDhombres functional equationNonstandard analysis and Ulam stabilityThis book is dedicated in memory of Stanilsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader's understanding of theories, methods, and techniques utilized to solve significant problems. Topics include:Sobolev SpacesMaximal monotone operatorsA theorem of Brezis-NirenbergOperator-norm convergence of the Trotter product formulaElliptic operators with infinitely many variablesPseudo-and quasiconvexities for nonsmooth functionAnisotropic surface measuresEulerian and Lagrangian variablesMultiple periodic solutions of Lagrangian systemsPorous medium equationNondiscrete Lassonde-Revalski principleGraduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg's fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.

Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research;

Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization.

Dedicated to Tosio Kato's 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics.

The book is well versed with the hottest research topics such as Lifetime of Coverage, Weighted Sensor Cover, k-Coverage, Heterogeneous Sensors, Barrier, Sweep and Partial Coverage, Mobile Sensors, Camera Sensors and Energy-Harvesting Sensors, and more.

This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory.

This volume presents some recent and principal developments related to computational intelligence and optimization methods in control.

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book.

Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research.

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics.

Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research.

2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg's habilitation thesis "Marktform und Gleichgewicht," which formed the roots of bilevel optimization.

2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg's habilitation thesis "Marktform und Gleichgewicht," which formed the roots of bilevel optimization.

Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science.

Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research;