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Nonsmooth Vector Functions and Continuous Optimization
A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.
Nonsmooth Analysis
The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and finally presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed; this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.
Nonlinear Optimization with Financial Applications
The book introduces the key ideas behind practical nonlinear optimization. Computational finance—an increasingly popular area of mathematics degree programmes—is combined here with the study of an important class of numerical techniques. The essentials of most currently popular algorithms are described and their performance is demonstrated on a range of optimization problems arising in financial mathematics. Theoretical convergence properties of methods are stated and formal proofs are provided in enough cases to be instructive rather than overwhelming. Practical behaviour of methods is illustrated by computational examples and discussions of efficiency, accuracy and computational costs. Supporting software for the examples and exercises is available
Nonlinear Integer Programming
It is not an exaggeration that much of what people devote in their hfe re solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. This book addresses the topic of the general nonlinear integer programming (NLIP). The overall goal of the book is to bring the state of the art of the theoretical foundations and solution methods of NLIP to readers who are interested in optimization, operations research and computer science. This book investigates the theory and solution methodologies for the general NLIP and provides the developments
Multiscale Optimization Methods and Applications
One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level.The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.
Monte Carlo Methods in Fuzzy Optimization
This book is a concise and readable introduction to Monte Carlo methods to find good approximate solutions to fuzzy optimization problems. Various basic applications and illustrative examples are presented in an understandable way. The aim of the book is to convince the reader that Monte Carlo methods can be useful in generating approximate solutions to fuzzy optimization problems.
Models and Algorithms for Global Optimization : Essays Dedicated to Antanas Žilinskas on the Occasion of His 60th Birthday
The research of Antanas Žilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Žilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.
Modelling in Mathematical Programming : Methodology and Techniques
This book provides basic tools for learning how to model in mathematical programming, from models without much complexity to complex system models. It presents a unique methodology for the building of an integral mathematical model, as well as new techniques that help build under own criteria. It allows readers to structure models from the elements and variables to the constraints, a basic modelling guide for any system with a new scheme of variables, a classification of constraints and also a set of rules to model specifications stated as logical propositions, helping to better understand models already existing in the literature. It also presents the modelling of all possible objectives that may arise in optimization problems regarding the variables values. The book is structured to guide the reader in an orderly manner, learning of the components that the methodology establishes in an optimization problem. The system includes the elements, which are all the actors that participate in the system, decision activities that occur in the system, calculations based on the decision activities, specifications such as regulations, impositions or actions of defined value and objective criterion, which guides the resolution of the system.
Metaheuristic Optimization via Memory and Evolution : Tabu Search and Scatter Search
Tabu Search (TS) and, more recently, Scatter Search (SS) have proved highly effective in solving a wide range of optimization problems, and have had a variety of applications in industry, science, and government. The goal of METAHEURISTIC OPTIMIZATION VIA MEMORY AND EVOLUTION: Tabu Search and Scatter Search is to report original research on algorithms and applications of tabu search, scatter search or both, as well as variations and extensions having "adaptive memory programming" as a primary focus. Individual chapters identify useful new implementations or new ways to integrate and apply the principles of TS and SS, or that prove new theoretical results, or describe the successful application of these methods to real world problems.The chapters of this book provide a series of landmarks along the way as we investigate and seek to better understand the elements of tabu search and scatter search that account for their successes in an astonishingly varied range of applications.
Metaheuristic Optimization Algorithms in Civil Engineering : New Applications
Discusses the application of metaheuristic algorithms in a number of important optimization problems in civil engineering. Advances in civil engineering technologies require greater accuracy, efficiency and speed in terms of the analysis and design of the corresponding systems. As such, it is not surprising that novel methods have been developed for the optimal design of real-world systems and models with complex configurations and large numbers of elements.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems ; Vol.3990 ; 3rd International Conference, CPAIOR 2006, Cork, Ireland, May 31 - June 2, 2006, Proceedings
Constitutes the refereed proceedings of the Third International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2006. The 20 revised full papers presented together with 3 invited talks address methodological and foundational issues from AI, OR, and algorithmics and present applications to the solution of combinatorial optimization problems in various fields via constraint programming.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems ; Vol.3524 : 2nd International Conference, CPAIOR 2005, Prague, Czech Republic, May 31 -- June 1, 2005
Intended primarily as a forum to focus on the integration and hybridization of the approaches of constraint programming (CP), arti?cial intelligence (AI), and operations research (OR) technologies for solving large-scale and complex real-life optimization problems. Therefore, CPAIOR is never far from industrial applications. The high number of submissions received this year, almost 100 papers, in witness to the interest of the research community in this conference. From these submissions, we chose 26 to be published in full in the proceedings. This volume includes summaries of the invited talks of CPAIOR: one from industry, one from the embedded system research community, and one from the operations research community.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems ; 5th International Conference, CPAIOR 2008 Paris, France, May 20-23, 2008 Proceedings
The 5th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2008) was held in Paris, France May 20–23, 2008. The purpose of this conference series is to bring together researchers in the felds of constraint programming, artifcial intelligence, and operations research to explore ways of solving large-scale, practical optimization problems through integration and hybridization of the felds’ diferent techniques. Through the years, this research community is discovering that the felds have much in c- mon, and there has been tremendous richness in the resulting cross-fertilization of felds.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems ; 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings
This book constitutes the refereed proceedings of the 4th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2007, held in Brussels, Belgium in May 2007.
Integrated Methods for Optimization
Integrated Methods for Optimization integrates the key concepts of Mathematical Programming and Constraint Programming into a unified framework that allows them to be generalized and combined. The unification of MP and CP creates optimization methods that have much greater modeling power, increased computational speed, and a sizeable reduction computational coding. Hence the benefits of this integration are substantial, providing the Applied Sciences with a powerful, high-level modeling solution for optimization problems. As reviewers of the book have noted, this integration along with constraint programming being incorporated into a number of programming languages, brings the field a step closer to being able to simply state a problem and having the computer solve it.
Hybrid metaheuristics ; 5th International Workshop, HM 2008, Málaga, Spain, October 8-9, 2008. Proceedings
This book constitutes the refereed proceedings of the 5th International Workshop on Hybrid Metaheuristics, HM 2008, held in Malaga, Spain, in October 2008.The 14 revised full papers presented were carefully reviewed and selected from 33 submissions. The papers discuss specific aspects of combinations of metaheuristics and other solving techniques for tackling particular relevant constrained optimization problems, such as fiber optic networks, time tabling and freight train scheduling problems.
Handbook of Combinatorial Optimization : Supplement ; Vol. B
It presents chapters dealing with various aspects of the subject, including optimization problems and algorithmic approaches for discrete problems.
Experimental Research in Evolutionary Computation : The New Experimentalism
This book introduces the new experimentalism in evolutionary computation, providing tools to understand algorithms and programs and their interaction with optimization problems. The book develops and applies statistical techniques to analyze and compare modern search heuristics such as evolutionary algorithms and particle swarm optimization. Treating optimization runs as experiments, the author offers methods for solving complex real-world problems that involve optimization via simulation, and he describes successful applications in engineering and industrial control projects.
Evolutionary Multi-Criterion Optimization ; 4th International Conference, EMO 2007, Matsushima, Japan, March 5-8, 2007, Proceedings
Multicriterion optimization refers to problems with two or more objectives (normally in conflict with each other) which must be simultaneously satisfied. Evolutionary algorithms have been used for solving multicriterion optimization problems for over two decades, gaining an increasing attention from industry. This book included four keynote speakers: Hirotaka Nakayama on aspiration level methods, Kay Chen Tan on large and computationally intensive real-world MO optimization problems, Carlos Fonseca on decision making, and Gary B. Lamont on design of large-scale network centric systems.
Efficient Approximation and Online Algorithms : Recent Progress on Classical Combinatorial Optimization Problems and New Applications
This book provides a good opportunity for computer science practitioners and researchers to get in sync with current state-of-the-art and future trends in the field of combinatorial optimization and online algorithms. Recent advances in this area are presented focusing on the design of efficient approximation and on-line algorithms. One central idea in the book is to use a linear program relaxation of the problem, randomization and rounding techniques.
