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检索条件"丛书名=Nonconvex Optimization and Its Applications"

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Developments in Global optimization 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Immanuel M. Bomze Tibor Csendes Reiner Horst Panos M. Pardalos

ISBN: (数字)9781475726008

ISBN: (纸本)9780792343516;9781441947680

In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented.;All researchers and students working in mathematical programming.

关键词： Software Engineering/Programming and Operating Systems optimization applications of Mathematics Computational Mathematics and Numerical Analysis Algorithms Operations Research/Decision Theory

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Convexification and Global optimization in Continuous and Mixed-Integer Nonlinear Programming 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Mohit Tawarmalani Nikolaos V. Sahinidis

ISBN: (数字)9781475735321

ISBN: (纸本)9781402010316;9781441952356

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

关键词： Mathematical Modeling and Industrial Mathematics Computational Mathematics and Numerical Analysis Data Structures optimization Numeric Computing Operations Research/Decision Theory

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Stochastic Decomposition 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Julia L. Higle Suvrajeet Sen

ISBN: (数字)9781461541158

ISBN: (纸本)9780792338406;9781461368458

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

关键词： optimization Operations Research/Decision Theory Systems Theory, Control

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Variational and Hemivariational Inequalities Theory, Methods and applications 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： D. Goeleven Y. Dumont M. Rochdi D. Motreanu

ISBN: (数字)9781441986108

ISBN: (纸本)9781402075377;9781461346463

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

关键词： Calculus of Variations and Optimal Control optimization Partial Differential Equations optimization applications of Mathematics Ordinary Differential Equations

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Advances in Convex Analysis and Global optimization 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Nicolas Hadjisavvas Panos M. Pardalos

ISBN: (数字)9781461302797

ISBN: (纸本)9780792369424;9781461379751

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

关键词： optimization Algorithms Mathematical Modeling and Industrial Mathematics

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Global optimization in Action 1

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丛书名： nonconvex optimization and its applications

1000年

作者： János D. Pintér

ISBN: (数字)9781475725025

ISBN: (纸本)9780792337577;9781441947512

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s).;provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on theauthor's research, in cooperation (on applications) with a number of colleagues.;Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

关键词： Mathematical Modeling and Industrial Mathematics optimization applications of Mathematics Systems Theory, Control

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Equilibrium Problems: Nonsmooth optimization and Variational Inequality Models 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Franco Giannessi Antonino Maugeri Panos M. Pardalos

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Bayesian Heuristic Approach to Discrete and Global optimization 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Jonas Mockus William Eddy Audris Mockus Linas Mockus Gintaras Reklaitis

ISBN: (数字)9781475726275

ISBN: (纸本)9780792343271;9781441947673

Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided.;: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.

关键词： Combinatorics optimization Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences applications of Mathematics

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Finite Element Method for Hemivariational Inequalities 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Jaroslav Haslinger Markku Miettinen Panagiotis D. Panagiotopoulos

ISBN: (数字)9781475752335

ISBN: (纸本)9780792359517;9781441948151

Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter.;: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.

关键词： Mathematics, general Classical Mechanics Mathematical and Computational Engineering

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Conjugate Gradient Algorithms in nonconvex optimization 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Radosław Pytlak

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