Recent Developments In Well Posed Variational Problems

Author : Roberto Lucchetti
Publisher : Springer Science & Business Media
ISBN 13 : 9401584729
Total Pages : 271 pages
Book Rating : 4.22/5 ( download)

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Download or read book Recent Developments in Well-Posed Variational Problems written by Roberto Lucchetti and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.

Author : Roberto Lucchetti
Publisher : Springer
ISBN 13 : 9789401584739
Total Pages : 268 pages
Book Rating : 4.37/5 ( download)

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Download or read book Recent Developments in Well-Posed Variational Problems written by Roberto Lucchetti and published by Springer. This book was released on 2013-01-11 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.

Author : Qamrul Hasan Ansari
Publisher : Springer Science & Business Media
ISBN 13 : 3642211143
Total Pages : 568 pages
Book Rating : 4.40/5 ( download)

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Download or read book Recent Developments in Vector Optimization written by Qamrul Hasan Ansari and published by Springer Science & Business Media. This book was released on 2011-09-21 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

Author : Michel Thera
Publisher : Springer Science & Business Media
ISBN 13 : 3642457800
Total Pages : 281 pages
Book Rating : 4.07/5 ( download)

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Download or read book Ill-posed Variational Problems and Regularization Techniques written by Michel Thera and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in the field of ill-posed variational problems and variational inequalities, covering a large range of theoretical, numerical and practical aspects. The main topics are: - Regularization techniques for equilibrium and fixed point problems, variational inequalities and complementary problems, - Links between approximation, penalization and regularization, - Bundle methods, nonsmooth optimization and regularization, - Error Bounds for regularized optimization problems.

Author : Mircea Sofonea
Publisher : Springer Nature
ISBN 13 : 3031414160
Total Pages : 410 pages
Book Rating : 4.69/5 ( download)

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Download or read book Well-Posed Nonlinear Problems written by Mircea Sofonea and published by Springer Nature. This book was released on 2023-11-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 0306480263
Total Pages : 304 pages
Book Rating : 4.63/5 ( download)

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Download or read book Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Author : Savin Treanta
Publisher :
ISBN 13 : 9783036565880
Total Pages : 0 pages
Book Rating : 4.84/5 ( download)

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Download or read book Variational Problems and Applications written by Savin Treanta and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current reprint presents studies of uncertain variational problems. It aims to develop the research in this field by formulating and demonstrating some characterization results of well-posedness and robust efficient solutions in new classes of (multiobjective) variational (control) problems governed by multiple and/or path-independent curvilinear integral cost functionals and robust mixed and/or isoperimetric constraints involving first- and second-order partial differential equations.

Author : Tomáš Roubiček
Publisher : Walter de Gruyter
ISBN 13 : 9783110145427
Total Pages : 496 pages
Book Rating : 4.21/5 ( download)

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Download or read book Relaxation in Optimization Theory and Variational Calculus written by Tomáš Roubiček and published by Walter de Gruyter. This book was released on 1997 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces applied mathematicians and graduate students to an original relaxation method based on a continuous extension of various optimization problems relating to convex compactification; it can be applied to problems in optimal control theory, the calculus of variations, and non-cooperative game theory. Reviews the background and summarizes the general theory of convex compactifications, then uses it to obtain convex, locally compact envelopes of the Lebesague and Sobolev spaces involved in concrete problems. The nontrivial envelopes cover the classical Young measures as well as various generalizations of them, which can record the limit behavior of fast oscillation and concentration effects. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Guang-ya Chen
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212898
Total Pages : 324 pages
Book Rating : 4.92/5 ( download)

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Download or read book Vector Optimization written by Guang-ya Chen and published by Springer Science & Business Media. This book was released on 2005-07-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.

Author : Anthony V. Fiacco
Publisher : CRC Press
ISBN 13 : 1000117111
Total Pages : 456 pages
Book Rating : 4.10/5 ( download)

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Download or read book Mathematical Programming with Data Perturbations written by Anthony V. Fiacco and published by CRC Press. This book was released on 2020-09-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.