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Author: Kiyotaka Shimizu
Publisher: Springer Science & Business Media
ISBN: 1461563054
Category : Business & Economics
Languages : en
Pages : 482
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Book Description
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.
Author: Kiyotaka Shimizu
Publisher: Springer Science & Business Media
ISBN: 1461563054
Category : Business & Economics
Languages : en
Pages : 482
Get Book Here
Book Description
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.
Author: Rossitza Setchi
Publisher: Springer Science & Business Media
ISBN: 3642153895
Category : Computers
Languages : en
Pages : 682
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Book Description
The four-volume set LNAI 6276--6279 constitutes the refereed proceedings of the 14th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2010, held in Cardiff, UK, in September 2010. The 272 revised papers presented were carefully reviewed and selected from 360 submissions. They present the results of high-quality research on a broad range of intelligent systems topics.
Author: Michael Hintermüller
Publisher: Springer Nature
ISBN: 3030793931
Category : Mathematics
Languages : en
Pages : 518
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Book Description
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.
Author: Georgios E. Stavroulakis
Publisher: Springer Science & Business Media
ISBN: 1461500192
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have a certain advantage for the construction of parametrized mechanical models. Both elastostatic and harmonic or transient dynamic problems are considered. The inverse problems are formulated as output error minimization problems and they are theoretically studied as a bilevel optimization problem, also known as a mathematical problem with equilibrium constraints. Beyond classical numerical optimization, soft computing tools (neural networks and genetic algorithms) and filter algorithms are used for the numerical solution. The book provides all the required material for the mathematical and numerical modeling of crack identification testing procedures in statics and dynamics and includes several thoroughly discussed applications, for example, the impact-echo nondestructive evaluation technique. Audience: The book will be of interest to structural and mechanical engineers involved in nondestructive testing and quality control projects as well as to research engineers and applied mathematicians who study and solve related inverse problems. People working on applied optimization and soft computing will find interesting problems to apply to their methods and all necessary material to continue research in this field.
Author: David Avis
Publisher: Springer Science & Business Media
ISBN: 9780387255910
Category : Business & Economics
Languages : en
Pages : 286
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Book Description
Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.
Author: Gianni Pillo
Publisher: Springer Science & Business Media
ISBN: 1475732260
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.
Author: Todor Stoilov
Publisher: Springer Science & Business Media
ISBN: 9400900171
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Multilevel decision theory arises to resolve the contradiction between increasing requirements towards the process of design, synthesis, control and management of complex systems and the limitation of the power of technical, control, computer and other executive devices, which have to perform actions and to satisfy requirements in real time. This theory rises suggestions how to replace the centralised management of the system by hierarchical co-ordination of sub-processes. All sub-processes have lower dimensions, which support easier management and decision making. But the sub-processes are interconnected and they influence each other. Multilevel systems theory supports two main methodological tools: decomposition and co-ordination. Both have been developed, and implemented in practical applications concerning design, control and management of complex systems. In general, it is always beneficial to find the best or optimal solution in processes of system design, control and management. The real tendency towards the best (optimal) decision requires to present all activities in the form of a definition and then the solution of an appropriate optimization problem. Every optimization process needs the mathematical definition and solution of a well stated optimization problem. These problems belong to two classes: static optimization and dynamic optimization. Static optimization problems are solved applying methods of mathematical programming: conditional and unconditional optimization. Dynamic optimization problems are solved by methods of variation calculus: Euler Lagrange method; maximum principle; dynamical programming.
Author: Stephan Dempe
Publisher: Springer Nature
ISBN: 3030521192
Category : Business & Economics
Languages : en
Pages : 679
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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.
Author: Shashi Kant Mishra
Publisher: CRC Press
ISBN: 1482255758
Category : Business & Economics
Languages : en
Pages : 509
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Book Description
Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.The book describes the characterizations of solution sets of various optimiza
Author: Juan Rosellón
Publisher: Springer Science & Business Media
ISBN: 1447147871
Category : Business & Economics
Languages : en
Pages : 442
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Book Description
Whilst financial rights have appeared as a successful ingredient in North-American power markets, they have their shortcomings both theoretically and in practice. Financial Transmission Rights: Analysis, Experiences and Prospects present a systematic and comprehensive overview of financial transmission rights (FTRS). Following a general introduction to FTRs, including chapters to explain transmission pricing and the general properties of FTRS, experts in the field provide discussions on wide scope of topics. These include: Varying perspectives on FTRS: from electrical engineers to economists, Different mathematical formulations of FTRS Financial Hedging using FTRS, and Alternative solutions to FTRs The detail, expertise and range of content makes Financial Transmission Rights: Analysis, Experiences and Prospect an essential resource for electricity market specialists both at academic and professional levels. “This is THE BOOK we were all expecting to address all key ‘Financial Transmission Rights’ issues. It is comprehensive and reader friendly. You can pick at will in its menu: more or less theory, a bit of maths or none, empirical review of real cases or numerical simulations of many feasible options. Big names rally there to delight you like: Hogan , Oren, Perez-Arriaga, Smeers, Hobbs and... Rosellón. More than a must read: a light house, a map and a survival kit.” Jean – Michel Glachant, Director Florence School, Holder Loyola de Palacio Chair, Chief-editor Economics of Energy & Environmental Policy. "In the last two decades, economists have developed a better understanding of the impact of financial rights on risk management, market power and network expansion in electricity markets, while power systems have experimented with such rights. Striking a good balance between academics and practitioners, always at the frontier of the field, written by the best experts, this volume is essential reading for all those- power systems’ managers and users, regulators, students and researchers- who want to understand the new electricity environment and predict its evolution." Jean Tirole, Toulouse School of Economics and Institute for Industrial Economics (IDEI) Further comments inside.
