This book is devoted to one of the main questions of the theory of extremal prob lems, namely, to necessary and sufficient extremality conditions. It is intended mostly for mathematicians and also for all those who are interested in optimiza tion problems. The book may be useful for advanced students, post-graduated students, and researchers. The book consists of four chapters. In Chap. 1 we study the abstract minimization problem with constraints, which is often called the mathemati cal programming problem. Chapter 2 is devoted to one of the most important classes of extremal problems, the optimal control problem. In the third chapter we study one of the main objects of the calculus of variations, the integral quadratic form. In the concluding, fourth, chapter we study local properties of smooth nonlinear mappings in a neighborhood of an abnormal point. The problems which are studied in this book (of course, in addition to their extremal nature) are united by our main interest being in the study of the so called abnormal or degenerate problems. This is the main distinction of the present book from a large number of books devoted to theory of extremal problems, among which there are many excellent textbooks, and books such as, e.g., [13, 38, 59, 78, 82, 86, 101, 112, 119], to mention a few.

This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.

Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints. The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.

This book constitutes the thoroughly refereed post-conference proceedings of the 11th International Conference on Large-Scale Scientific Computations, LSSC 2017, held in Sozopol, Bulgaria, in June 2017. The 63 revised short papers together with 3 full papers presented were carefully reviewed and selected from 63 submissions. The conference presents results from the following topics: Hierarchical, adaptive, domain decomposition and local refinement methods; Robust preconditioning algorithms; Monte Carlo methods and algorithms; Numerical linear algebra; Control and optimization; Parallel algorithms and performance analysis; Large-scale computations of environmental, biomedical and engineering problems. The chapter 'Parallel Aggregation Based on Compatible Weighted Matching for AMG' is available open access under a CC BY 4.0 license.

This book constitutes the refereed proceedings of the 10th International Conference on Optimization and Applications, OPTIMA 2019, held in Petrovac, Montenegro, in September-October 2019. The 35 revised full papers presented were carefully reviewed and selected from 117 submissions. The papers cover such topics as optimization, operations research, optimal control, game theory, and their numerous applications in practical problems of operations research, data analysis, and software development.

This book is a collection of thoroughly refereed papers presented at the 25th IFIP TC 7 Conference on System Modeling and Optimization, held in Dresden, Germany, in September 2011. The 55 revised papers were carefully selected from numerous submissions. They are organized in the following topical sections: control of distributed parameter systems; stochastic optimization and control; stabilization, feedback, and model predictive control; flow control; shape and structural optimization; and applications and control of lumped parameter systems.

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

This book presents the proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019, September 16 – 20, 2019, Yekaterinburg, Russia), organized by the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. Discussing the latest advances in the theory of optimal control, stability theory and differential games, it also demonstrates the application of new techniques and numerical algorithms to solve problems in robotics, mechatronics, power and energy systems, economics and ecology. Further, the book includes fundamental results in control theory, stability theory and differential games presented at the conference, as well as a number of chapters focusing on novel approaches in solving important applied problems in control and optimization. Lastly, it evaluates recent major accomplishments, and forecasts developments in various up-and-coming areas, such as hybrid systems, model predictive control, Hamilton–Jacobi equations and advanced estimation algorithms.