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

共 105 条记录，以下是61-70 订阅

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Quasidifferentiability and Related Topics 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： Vladimir Demyanov Alexander Rubinov

ISBN: (数字)9781475731378

ISBN: (纸本)9780792362845;9781441948304

2 Radiant sets 236 3 Co-radiant sets 239 4 Radiative and co-radiative sets 241 5 Radiant sets with Lipschitz continuous Minkowski gauges 245 6 Star-shaped sets and their kernels 249 7 Separation 251 8 Abstract convex star-shaped sets 255 References 260 11 DIFFERENCES OF CONVEX COMPACTA AND METRIC SPACES OF CON- 263 VEX COMPACTA WITH applications: A SURVEY A. M. Rubinov, A. A. Vladimirov 1 Introduction 264 2 Preliminaries 264 3 Differences of convex compact sets: general approach 266 4 Metric projections and corresponding differences (one-dimensional case) 267 5 The *-difference 269 6 The Demyanov difference 271 7 Geometric and inductive definitions of the D-difference 273 8 applications to DC and quasidifferentiable functions 276 9 Differences of pairs of set-valued mappings with applications to quasidiff- entiability 278 10 applications to approximate subdifferentials 280 11 applications to the approximation of linear set-valued mappings 281 12 The Demyanov metric 282 13 The Bartels-Pallaschke metric 284 14 Hierarchy of the three norms on Qn 285 15 Derivatives 287 16 Distances from convex polyhedra and convergence of convex polyhedra 289 17 Normality of convex sets 290 18 D-regular sets 291 19 Variable D-regular sets 292 20 optimization 293 References 294 12 CONVEX APPROXIMATORS.

关键词： Industrial and Production Engineering Calculus of Variations and Optimal Control optimization Analysis Mathematical Modeling and Industrial Mathematics

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Smooth Nonlinear optimization in 1

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丛书名： nonconvex optimization and its applications

1000年

作者： Tamás Rapcsák

ISBN: (数字)9781461563570

ISBN: (纸本)9780792346807;9781461379201

Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.

关键词： optimization Software Engineering/Programming and Operating Systems Probability Theory and Stochastic Processes Operations Research/Decision Theory Differential Geometry Convex and Discrete Geometry

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Semi-Infinite Programming 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： Rembert Reemtsen Jan-J. Rückmann

ISBN: (数字)9781475728682

ISBN: (纸本)9780792350545;9781441947956

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming. SIP problems include finitely many variables and, in contrast to finite optimization problems, infinitely many inequality constraints. Prob lems of this type naturally arise in approximation theory, optimal control, and at numerous engineering applications where the model contains at least one inequality constraint for each value of a parameter and the parameter, repre senting time, space, frequency etc., varies in a given domain. The treatment of such problems requires particular theoretical and numerical techniques. The theory in SIP as well as the number of numerical SIP methods and appli cations have expanded very fast during the last years. Therefore, the main goal of this monograph is to provide a collection of tutorial and survey type articles which represent a substantial part of the contemporary body of knowledge in SIP. We are glad that leading researchers have contributed to this volume and that their articles are covering a wide range of important topics in this subject. It is our hope that both experienced students and scientists will be well advised to consult this volume. We got the idea for this volume when we were organizing the semi-infinite pro gramming workshop which was held in Cottbus, Germany, in September 1996.

关键词： Software Engineering/Programming and Operating Systems optimization Operations Research/Decision Theory Operations Research, Management Science Mathematical Modeling and Industrial Mathematics

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Quadratic Programming and Affine Variational Inequalities 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： Gue Myung Lee Nguyen Nang Tam Nguyen Dong Yen

ISBN: (数字)9780387242781

ISBN: (纸本)9780387242774;9781441937131

Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.

关键词： optimization Operations Research, Management Science Operations Research/Decision Theory

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Large-Scale Nonlinear optimization 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： G. Pillo M. Roma

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Generalized Convexity, Generalized Monotonicity and applications 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： Andrew Eberhard Nicolas Hadjisavvas Dinh The Luc

ISBN: (数字)9780387236391

ISBN: (纸本)9780387236384;9781441936479

In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://***) consists of more than 300 researchers coming from 36 countries.

关键词： Operations Research, Management Science optimization Calculus of Variations and Optimal Control optimization Game Theory, Economics, Social and Behav. Sciences

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Approximation and Complexity in Numerical optimization 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： Panos M. Pardalos

ISBN: (数字)9781475731453

ISBN: (纸本)9780792362753;9781441948298

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied optimization of the University of Florida.

关键词： Industrial and Production Engineering Calculus of Variations and Optimal Control optimization Theory of Computation Approximations and Expansions

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Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： D. Motreanu V. Rǎdulescu

ISBN: (数字)9781475769210

ISBN: (纸本)9781402013850;9781441952486

This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.

关键词： Calculus of Variations and Optimal Control optimization optimization Partial Differential Equations Functional Analysis Ordinary Differential Equations

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optimization in Computational Chemistry and Molecular Biology 1

引用

丛书名： nonconvex optimization and its applications

1000年

作者： C. A. Floudas P. M. Pardalos

ISBN: (数字)9781475732184

ISBN: (纸本)9780792361558;9781441948267

covers recent developments in optimization techniques for addressing several computational chemistry and biology problems. A tantalizing problem that cuts across the fields of computational chemistry, biology, medicine, engineering and applied mathematics is how proteins fold. Global and local optimization provide a systematic framework of conformational searches for the prediction of three-dimensional protein structures that represent the global minimum free energy, as well as low-energy biomolecular conformations.;Each contribution in the book is essentially expository in nature, but of scholarly treatment. The topics covered include advances in local and global optimization approaches for molecular dynamics and modeling, distance geometry, protein folding, molecular structure refinement, protein and drug design, and molecular and peptide docking.;The book is addressed not only to researchers in mathematical programming, but to all scientists in various disciplines who use optimization methods in solving problems in computational chemistry and biology.

关键词： Software Engineering/Programming and Operating Systems optimization applications of Mathematics Algorithms Mathematical Modeling and Industrial Mathematics Mathematics, general

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Variational and Hemivariational Inequalities 1

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丛书名： nonconvex optimization and its applications

1000年

作者： D. Goeleven D. Motreanu

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