Optimality Conditions Abnormal And Degenerate Problems

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Optimality Conditions: Abnormal and Degenerate Problems

Aram Arutyunov
Optimality Conditions Abnormal and Degenerate Problems Book PDF

Author : Aram Arutyunov
Publisher : Springer
Page : 300 pages
File Size : 51,6 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 9401594392

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Optimality Conditions: Abnormal and Degenerate Problems by Aram Arutyunov Pdf

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.

Optimality Conditions: Abnormal and Degenerate Problems

A.V. Arutyunov
Optimality Conditions Abnormal and Degenerate Problems Book PDF

Author : A.V. Arutyunov
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 43,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401594387

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Optimality Conditions: Abnormal and Degenerate Problems by A.V. Arutyunov Pdf

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.

Optimal Impulsive Control

Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira
Optimal Impulsive Control Book PDF

Author : Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira
Publisher : Springer
Page : 174 pages
File Size : 40,7 Mb
Release : 2018-12-17
Category : Technology & Engineering
ISBN : 9783030022600

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Optimal Impulsive Control by Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira Pdf

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.

Large-Scale Scientific Computing

Ivan Lirkov,Svetozar Margenov
Large Scale Scientific Computing Book PDF

Author : Ivan Lirkov,Svetozar Margenov
Publisher : Springer
Page : 610 pages
File Size : 50,8 Mb
Release : 2018-01-10
Category : Computers
ISBN : 9783319734415

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Large-Scale Scientific Computing by Ivan Lirkov,Svetozar Margenov Pdf

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.

System Modeling and Optimization

Dietmar Hömberg,Fredi Tröltzsch
System Modeling and Optimization Book PDF

Author : Dietmar Hömberg,Fredi Tröltzsch
Publisher : Springer
Page : 568 pages
File Size : 41,9 Mb
Release : 2013-02-20
Category : Computers
ISBN : 9783642360626

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System Modeling and Optimization by Dietmar Hömberg,Fredi Tröltzsch Pdf

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.

Stability, Control and Differential Games

Alexander Tarasyev,Vyacheslav Maksimov,Tatiana Filippova
Stability Control and Differential Games Book PDF

Author : Alexander Tarasyev,Vyacheslav Maksimov,Tatiana Filippova
Publisher : Springer Nature
Page : 380 pages
File Size : 49,5 Mb
Release : 2020-05-29
Category : Technology & Engineering
ISBN : 9783030428310

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Stability, Control and Differential Games by Alexander Tarasyev,Vyacheslav Maksimov,Tatiana Filippova Pdf

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.

Traces and Emergence of Nonlinear Programming

Giorgio Giorgi,Tinne Hoff Kjeldsen
Traces and Emergence of Nonlinear Programming Book PDF

Author : Giorgio Giorgi,Tinne Hoff Kjeldsen
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 55,7 Mb
Release : 2013-12-04
Category : Computers
ISBN : 9783034804394

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Traces and Emergence of Nonlinear Programming by Giorgio Giorgi,Tinne Hoff Kjeldsen Pdf

The book contains reproductions of the most important papers that gave birth to the first developments in nonlinear programming. Of particular interest is W. Karush's often quoted Master Thesis, which is published for the first time. The anthology includes an extensive preliminary chapter, where the editors trace out the history of mathematical programming, with special reference to linear and nonlinear programming.​

Analytical Solutions for Extremal Space Trajectories

Dilmurat M. Azimov
Analytical Solutions for Extremal Space Trajectories Book PDF

Author : Dilmurat M. Azimov
Publisher : Butterworth-Heinemann
Page : 330 pages
File Size : 42,5 Mb
Release : 2017-08-23
Category : Technology & Engineering
ISBN : 9780128140598

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Analytical Solutions for Extremal Space Trajectories by Dilmurat M. Azimov Pdf

Analytical Solutions for Extremal Space Trajectories presents an overall treatment of the general optimal control problem, in particular, the Mayer’s variational problem, with necessary and sufficient conditions of optimality. It also provides a detailed derivation of the analytical solutions of these problems for thrust arcs for the Newtonian, linear central and uniform gravitational fields. These solutions are then used to analytically synthesize the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers. Many numerical examples utilizing the proposed analytical synthesis of the space trajectories and comparison analyses with numerically integrated solutions are provided. This book will be helpful for engineers and researchers of industrial and government organizations, and is also a great resource for university faculty and graduate and undergraduate students working, specializing or majoring in the fields of aerospace engineering, applied celestial mechanics, and guidance, navigation and control technologies, applied mathematics and analytical dynamics, and avionics software design and development. Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers Assists in developing the optimal control theory for applications in aerospace technology and space mission design

Topological Aspects of Nonsmooth Optimization

Vladimir Shikhman
Topological Aspects of Nonsmooth Optimization Book PDF

Author : Vladimir Shikhman
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 50,9 Mb
Release : 2011-11-18
Category : Mathematics
ISBN : 9781461418979

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Topological Aspects of Nonsmooth Optimization by Vladimir Shikhman Pdf

This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory. ​ ​

Newton-Type Methods for Optimization and Variational Problems

Alexey F. Izmailov,Mikhail V. Solodov
Newton Type Methods for Optimization and Variational Problems Book PDF

Author : Alexey F. Izmailov,Mikhail V. Solodov
Publisher : Springer
Page : 573 pages
File Size : 46,9 Mb
Release : 2014-07-08
Category : Business & Economics
ISBN : 9783319042473

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Newton-Type Methods for Optimization and Variational Problems by Alexey F. Izmailov,Mikhail V. Solodov Pdf

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Developments in Model-Based Optimization and Control

Sorin Olaru,Alexandra Grancharova,Fernando Lobo Pereira
Developments in Model Based Optimization and Control Book PDF

Author : Sorin Olaru,Alexandra Grancharova,Fernando Lobo Pereira
Publisher : Springer
Page : 381 pages
File Size : 53,7 Mb
Release : 2015-12-23
Category : Technology & Engineering
ISBN : 9783319266879

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Developments in Model-Based Optimization and Control by Sorin Olaru,Alexandra Grancharova,Fernando Lobo Pereira Pdf

This book deals with optimization methods as tools for decision making and control in the presence of model uncertainty. It is oriented to the use of these tools in engineering, specifically in automatic control design with all its components: analysis of dynamical systems, identification problems, and feedback control design. Developments in Model-Based Optimization and Control takes advantage of optimization-based formulations for such classical feedback design objectives as stability, performance and feasibility, afforded by the established body of results and methodologies constituting optimal control theory. It makes particular use of the popular formulation known as predictive control or receding-horizon optimization. The individual contributions in this volume are wide-ranging in subject matter but coordinated within a five-part structure covering material on: · complexity and structure in model predictive control (MPC); · collaborative MPC; · distributed MPC; · optimization-based analysis and design; and · applications to bioprocesses, multivehicle systems or energy management. The various contributions cover a subject spectrum including inverse optimality and more modern decentralized and cooperative formulations of receding-horizon optimal control. Readers will find fourteen chapters dedicated to optimization-based tools for robustness analysis, and decision-making in relation to feedback mechanisms—fault detection, for example—and three chapters putting forward applications where the model-based optimization brings a novel perspective. Developments in Model-Based Optimization and Control is a selection of contributions expanded and updated from the Optimisation-based Control and Estimation workshops held in November 2013 and November 2014. It forms a useful resource for academic researchers and graduate students interested in the state of the art in predictive control. Control engineers working in model-based optimization and control, particularly in its bioprocess applications will also find this collection instructive.

Quantum Variational Calculus

Agnieszka B. Malinowska,Delfim F.M. Torres
Quantum Variational Calculus Book PDF

Author : Agnieszka B. Malinowska,Delfim F.M. Torres
Publisher : Springer Science & Business Media
Page : 84 pages
File Size : 42,6 Mb
Release : 2013-11-29
Category : Mathematics
ISBN : 9783319027470

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Quantum Variational Calculus by Agnieszka B. Malinowska,Delfim F.M. Torres Pdf

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.

Optimization and Applications

Milojica Jaćimović,Michael Khachay,Vlasta Malkova,Mikhail Posypkin
Optimization and Applications Book PDF

Author : Milojica Jaćimović,Michael Khachay,Vlasta Malkova,Mikhail Posypkin
Publisher : Springer Nature
Page : 515 pages
File Size : 52,8 Mb
Release : 2020-01-08
Category : Computers
ISBN : 9783030386030

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Optimization and Applications by Milojica Jaćimović,Michael Khachay,Vlasta Malkova,Mikhail Posypkin Pdf

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.

Optimization and Applications

Nicholas Olenev,Yuri Evtushenko,Milojica Jaćimović,Michael Khachay,Vlasta Malkova
Optimization and Applications Book PDF

Author : Nicholas Olenev,Yuri Evtushenko,Milojica Jaćimović,Michael Khachay,Vlasta Malkova
Publisher : Springer Nature
Page : 401 pages
File Size : 41,7 Mb
Release : 2023-12-11
Category : Mathematics
ISBN : 9783031478598

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Optimization and Applications by Nicholas Olenev,Yuri Evtushenko,Milojica Jaćimović,Michael Khachay,Vlasta Malkova Pdf

This book constitutes the refereed proceedings of the 14th International Conference on Optimization and Applications, OPTIMA 2023, held in Petrovac, Montenegro, during September 18–22, 2023. The 27 full papers included in this book were carefully reviewed and selected from 68 submissions. They were organized in topical sections as follows: ​mathematical programming; global optimization; discrete and combinatorial optimization; game theory and mathematical economics; optimization in economics and finance; and applications.

Variational Analysis and Generalized Differentiation II

Boris S. Mordukhovich
Variational Analysis and Generalized Differentiation II Book PDF

Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Page : 630 pages
File Size : 50,5 Mb
Release : 2006-03-02
Category : Mathematics
ISBN : 9783540312468

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Variational Analysis and Generalized Differentiation II by Boris S. Mordukhovich Pdf

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.