Download or read book On Minimal Pairs of Compact Convex Sets and of Convex Functions written by Semu Mitiku Kassa and published by . This book was released on 2002 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pairs of Compact Convex Sets written by Diethard Ernst Pallaschke and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Rådström-Hörmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the Rådström-Hörmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs.
Download or read book Pairs of Compact Convex Sets written by Diethard Pallaschke and published by . This book was released on 2014-01-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Sets and Their Applications written by Steven R. Lay and published by Courier Corporation. This book was released on 2007-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity. It leads students to open questions and unsolved problems, and it highlights diverse applications. Author Steven R. Lay, Professor of Mathematics at Lee University in Tennessee, reinforces his teachings with numerous examples, plus exercises with hints and answers. The first three chapters form the foundation for all that follows, starting with a review of the fundamentals of linear algebra and topology. They also survey the development and applications of relationships between hyperplanes and convex sets. Subsequent chapters are relatively self-contained, each focusing on a particular aspect or application of convex sets. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Hints, solutions, and references for the exercises appear at the back of the book.
Download or read book Function Spaces written by Henryk Hudzik and published by CRC Press. This book was released on 2000-07-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.
Download or read book Quasidifferentiability and Related Topics written by Vladimir F. Demyanov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Convex Bodies The Brunn Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Download or read book Convex and Fractal Geometry written by Robert J. MacG. Dawson and published by . This book was released on 2009 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference Convex and Fractal Geometry was held at the Stefan Banach International Mathematical Center at Bedlewo, May 21-26, 2007. ... This volume contains twelve papers related to the talks delivered at that conference.
Download or read book Foundations of Mathematical Optimization written by Diethard Ernst Pallaschke and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.
Download or read book Recent Advances in Optimization written by Peter Gritzmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent theoretical and practical aspects in the field of optimization and convex analysis. The topics covered in this volume include: - Equilibrium models in economics. - Control theory and semi-infinite programming. - Ill-posed variational problems. - Global optimization. - Variational methods in image restoration. - Nonsmooth optimization. - Duality theory in convex and nonconvex optimization. - Methods for large scale problems.
Download or read book Compact Convex Sets and Boundary Integrals written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop -de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and tech nically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominated extension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral for mulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applica tions, in particular to operator theory and function algebras.
Download or read book Function Spaces written by Ryszard Grz??lewicz and published by World Scientific. This book was released on 2003 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers included in this volume deal with the following topics: convex analysis, operator theory, interpolation theory, theory of real functions, theory of analytic functions, bifurcation theory, Fourier analysis, functional analysis, measure theory, geometry of Banach spaces, history of mathematics.
Download or read book Function Spaces Proceedings Of The Sixth Conference written by Ryszard Grzaslewicz and published by World Scientific. This book was released on 2003-04-03 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers included in this volume deal with the following topics: convex analysis, operator theory, interpolation theory, theory of real functions, theory of analytic functions, bifurcation theory, Fourier analysis, functional analysis, measure theory, geometry of Banach spaces, history of mathematics.
Download or read book Variational Analysis and Applications written by Franco Giannessi and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 1163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.
Download or read book Undergraduate Convexity written by Niels Lauritzen and published by World Scientific. This book was released on 2013 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.Starting from linear inequalities and FourierOCoMotzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the KarushOCoKuhnOCoTucker conditions, duality and an interior point algorithm.
Download or read book Some Criteria for the Minimality of Pairs of Compact Convex Sets written by Diethard Pallaschke and published by . This book was released on 1991 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Easy Path to Convex Analysis and Applications written by Boris Mordukhovich and published by Springer Nature. This book was released on 2023-06-16 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.
