Download or read book Constrained Optimization and Image Space Analysis written by Franco Giannessi and published by Springer Science & Business Media. This book was released on 2006-10-27 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers. Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light. It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.

Download or read book Constrained Optimization and Image Space Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Constrained Optimization and Image Space Analysis Separation of sets and optimality conditions written by F. Giannessi and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.

Download or read book Nonlinear Analysis and Optimization II written by Simeon Reich and published by American Mathematical Soc.. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics. This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted to nonlinear analysis. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: J.-P. Aubin and S. Martin -- Travel time tubes regulating transportation traffic; R. Baier and E. Farkhi -- The directed subdifferential of DC functions; Z. Balanov, W. Krawcewicz, and H. Ruan -- Periodic solutions to $O(2)$-symmetric variational problems: $O(2) \times S^1$- equivariant gradient degree approach; J. F. Bonnans and N. P. Osmolovskii -- Quadratic growth conditions in optimal control problems; J. M. Borwein and S. Sciffer -- An explicit non-expansive function whose subdifferential is the entire dual ball; G. Buttazzo and G. Carlier -- Optimal spatial pricing strategies with transportation costs; R. A. C. Ferreira and D. F. M. Torres -- Isoperimetric problems of the calculus of variations on time scales; M. Foss and N. Randriampiry -- Some two-dimensional $\mathcal A$-quasiaffine functions; F. Giannessi, A. Moldovan, and L. Pellegrini -- Metric regular maps and regularity for constrained extremum problems; V. Y. Glizer -- Linear-quadratic optimal control problem for singularly perturbed systems with small delays; T. Maruyama -- Existence of periodic solutions for Kaldorian business fluctuations; D. Mozyrska and E. Paw'uszewicz -- Delta and nabla monomials and generalized polynomial series on time scales; D. Pallaschke and R. Urba'ski -- Morse indexes for piecewise linear functions; J.-P. Penot -- Error bounds, calmness and their applications in nonsmooth analysis; F. Rampazzo -- Commutativity of control vector fields and ""inf-commutativity""; A. J. Zaslavski -- Stability of exact penalty for classes of constrained minimization problems in finite-dimensional spaces. (CONM/514)

Download or read book Applications of Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-29 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.

Download or read book Nonlinear Analysis and Variational Problems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Download or read book Engineering and Applied Sciences Optimization written by Nikos D. Lagaros and published by Springer. This book was released on 2015-05-22 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters which appear in this volume are selected studies presented at the First International Conference on Engineering and Applied Sciences Optimization (OPT-i), Kos, Greece, 4-6 June 2014 and works written by friends, former colleagues and students of the late Professor M. G. Karlaftis; all in the area of optimization that he loved and published so much in himself. The subject areas represented here range from structural optimization, logistics, transportation, traffic and telecommunication networks to operational research, metaheuristics, multidisciplinary and multiphysics design optimization, etc. This volume is dedicated to the life and the memory of Professor Matthew G. Karlaftis, who passed away a few hours before he was to give the opening speech at OPT-i. All contributions reflect the warmth and genuine friendship which he enjoyed from his associates and show how much his scientific contribution has been appreciated. He will be greatly missed and it is hoped that this volume will be received as a suitable memorial to his life and achievements.

Download or read book Overcoming the Failure of the Classical Generalized Interior point Regularity Conditions in Convex Optimization written by Ernö Robert Csetnek and published by Logos Verlag Berlin GmbH. This book was released on 2010-06-30 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to present several new results concerning duality in scalar convex optimization, the formulation of sequential optimality conditions and some applications of the duality to the theory of maximal monotone operators. After recalling some properties of the classical generalized interiority notions which exist in the literature, we give some properties of the quasi interior and quasi-relative interior, respectively. By means of these notions we introduce several generalized interior-point regularity conditions which guarantee Fenchel duality. By using an approach due to Magnanti, we derive corresponding regularity conditions expressed via the quasi interior and quasi-relative interior which ensure Lagrange duality. These conditions have the advantage to be applicable in situations when other classical regularity conditions fail. Moreover, we notice that several duality results given in the literature on this topic have either superfluous or contradictory assumptions, the investigations we make offering in this sense an alternative. Necessary and sufficient sequential optimality conditions for a general convex optimization problem are established via perturbation theory. These results are applicable even in the absence of regularity conditions. In particular, we show that several results from the literature dealing with sequential optimality conditions are rediscovered and even improved. The second part of the thesis is devoted to applications of the duality theory to enlargements of maximal monotone operators in Banach spaces. After establishing a necessary and sufficient condition for a bivariate infimal convolution formula, by employing it we equivalently characterize the $\varepsilon$-enlargement of the sum of two maximal monotone operators. We generalize in this way a classical result concerning the formula for the $\varepsilon$-subdifferential of the sum of two proper, convex and lower semicontinuous functions. A characterization of fully en.

Download or read book Introduction to the Theory of Nonlinear Optimization written by Johannes Jahn and published by Springer Nature. This book was released on 2020-07-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Download or read book Vector Variational Inequalities and Vector Optimization written by Qamrul Hasan Ansari and published by Springer. This book was released on 2017-10-31 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Download or read book Fixed Point Theory Variational Analysis and Optimization written by Saleh Abdullah R. Al-Mezel and published by CRC Press. This book was released on 2014-06-03 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol

Download or read book Basic Mathematical Programming Theory written by Giorgio Giorgi and published by Springer Nature. This book was released on 2023-07-18 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.

Download or read book Lagrange type Functions in Constrained Non Convex Optimization written by Alexander M. Rubinov and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a mini mum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions.

Download or read book Optimization and Applications written by Nicholas N. Olenev and published by Springer Nature. This book was released on 2021-11-04 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Optimization and Applications, OPTIMA 2021, held in Petrovac, Montenegro, in September-October 2021. The 22 full and 3 short papers presented were carefully reviewed and selected from 63 submissions. The papers are organized into the following topical sub-headings: mathematical programming, global optimization, discrete and combinatorial optimization, optimal control, optimization and data analysis, and game theory and mathematical economics.

Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich and published by SIAM. This book was released on 2011-07-28 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.

Download or read book Computer Analysis of Images and Patterns written by Ainhoa Berciano and published by Springer. This book was released on 2011-08-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 6854/6855 constitutes the refereed proceedings of the International Conference on Computer Analysis of Images and Patterns, CAIP 2011, which took place in Seville, Spain, August 29-31, 2011. The 138 papers presented together with 2 invited talks were carefully reviewed and selected from 286 submissions. The papers are organized in topical section on: motion analysis, image and shape models, segmentation and grouping, shape recovery, kernel methods, medical imaging, structural pattern recognition, Biometrics, image and video processing, calibration; and tracking and stereo vision.