Books in the Springer Optimization and Its Applications series

This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material.Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano-Sussmann Orbit theorem, Rashevskii-Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.

Based on the "Third International Conference on Dynamics of Disasters" held in Kalamata, Greece, July 2017, this Work includes contributions in evacuation logistics, disaster communications between first responders, disaster relief, and a case study on humanitarian logistics.

The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. multistage time-delay systems and switched time-delay systems - for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed.

With comprehensive treatment of applied mathematical modeling in economics, population biology, and environmental science, this popular publication has been updated to textbook format for its second edition, which emphasizes control and optimization.

This book focuses on the nonlinear behavior of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings, using a numerical approach to analyze branching points and to build bifurcation paths.

Software Engineering Techniques Applied to Agricultural Systems presents cutting-edge software engineering techniques for designing and implementing better agricultural software systems based on the object-oriented paradigm and the Unified Modeling Language (UML).

This book presents papers surrounding the extensive discussions that took place from the ¿Variational Analysis and Aerospace Engineering¿ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

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

This book presents a variety of methods used in multidimensional data visualization. It details new research results and trends in the field, including optimization, artificial neural networks, combinations of algorithms, and parallel computing.

Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

This book presents papers surrounding the extensive discussions that took place from the 'Variational Analysis and Aerospace Engineering' workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author's lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin's fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems. Topics covered in this work include:· Algorithmic aspects of problems with disjoint cycles in graphs· Graphs where maximal cliques and stable sets intersect· The maximum independent set problem with special classes· A general technique for heuristic algorithms for optimization problems · The network design problem with cut constraints· Algorithms for computing the frustration index of a signed graph· A heuristic approach for studying the patrol problem on a graph· Minimum possible sum and product of the proper connection number· Structural and algorithmic results on branchings in digraphs · Improved upper bounds for Korkel--Ghosh benchmark SPLP instances

This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems.

Computational and theoretical open problems in optimization, computational geometry, data science, logistics, statistics, supply chain modeling, and data analysis are examined in this book. Each contribution provides the fundamentals needed to fully comprehend the impact of individual problems. Current theoretical, algorithmic, and practical methods used to circumvent each problem are provided to stimulate a new effort towards innovative and efficient solutions. Aimed towards graduate students and researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, this book provides a broad comprehensive approach to understanding the significance of specific challenging or open problems within each discipline. The contributions contained in this book are based on lectures focused on ¿Challenges and Open Problems in Optimization and Data Science¿ presented at the Deucalion Summer Institute for Advanced Studies in Optimization, Mathematics, and Data Science in August 2016.

Whether different types of costs are to be reduced, benefits to be maximized or scarce resources to be managed, scheduling theory provides intelligent methods for practitioners and scientists.

This book examines recent results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The material presented here offers new methods of identifying these solutions and studying their properties.

The connected dominating set has been a classic subject studied in graph theory since 1975. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics.

This book presents some recent systems engineering and mathematical tools for health care along with their real-world applications by health care practitioners and engineers. Systems Analysis Tools for Better Health Care Delivery illustrates the increased need of partnership between engineers and health care professionals.

Statistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems.

This selection of key studies covering numerous core challenges in space engineering addresses classic space application problems, such as trajectory optimization, alongside new ones including multidisciplinary design optimization and optimal control theory.

Chapters 9-13 are related to nondifferentiable optimization, and the volume concludes with four chapters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization: Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov.

The increasing complexity of financial problems and the enormous volume of financial data often make it difficult to apply traditional modeling and algorithmic procedures.

Unlike other books on theoretical computer science, this textbook organizes approximation algorithms into chapters based on the design techniques for the algorithms. This allows the reader to study approximation algorithms of the same nature together.

The Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at International School of Mathematics, Guido Stampacchia provided a platform for aerospace engineers and mathematicians to discuss the problems requiring an extensive application of mathematics. This work contains papers presented at the workshop.

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician.

This is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. Throughout the text, examples help readers make the bridge from theory to application. Numerous exercises are also offered to enable readers to apply and build their own skills and knowledge.