Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
Author: F. Giannessi
Publisher: Springer Science & Business Media
Total Pages: 304
Release: 2006-04-11
Genre: Mathematics
ISBN: 0306480263

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.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models
Author: P. Daniele
Publisher: Springer Science & Business Media
Total Pages: 468
Release: 2003-06-30
Genre: Mathematics
ISBN: 9781402074707

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models
Author: P. Daniele
Publisher: Springer Science & Business Media
Total Pages: 450
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461302390

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization
Author: Qamrul Hasan Ansari
Publisher: CRC Press
Total Pages: 294
Release: 2013-07-18
Genre: Business & Economics
ISBN: 1439868212

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.The first part of the book focuses on generalized convexity and generalized

Generalized Convexity and Vector Optimization

Generalized Convexity and Vector Optimization
Author: Shashi K. Mishra
Publisher: Springer Science & Business Media
Total Pages: 298
Release: 2008-12-19
Genre: Mathematics
ISBN: 3540856714

The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, in ?nite and in?nite dimensions. The problems include are nonlinear vector optimization problems, s- metric dual problems, continuous-time vector optimization problems, relationships between vector optimization and variational inequality problems. Nonlinear vector optimization problems arise in several contexts such as in the building and interpretation of economic models; the study of various technolo- cal processes; the development of optimal choices in ?nance; management science; production processes; transportation problems and statistical decisions, etc. In preparing this lecture note a special effort has been made to obtain a se- contained treatment of the subjects; so we hope that this may be a suitable source for a beginner in this fast growing area of research, a semester graduate course in nonlinear programing, and a good reference book. This book may be useful to theoretical economists, engineers, and applied researchers involved in this area of active research. The lecture note is divided into eight chapters: Chapter 1 brie?y deals with the notion of nonlinear programing problems with basic notations and preliminaries. Chapter 2 deals with various concepts of convex sets, convex functions, invex set, invex functions, quasiinvex functions, pseudoinvex functions, type I and generalized type I functions, V-invex functions, and univex functions.

Mathematical Analysis, Differential Equations And Applications

Mathematical Analysis, Differential Equations And Applications
Author: Panos M Pardalos
Publisher: World Scientific
Total Pages: 958
Release: 2024-07-26
Genre: Mathematics
ISBN: 9811267057

This comprehensive volume presents essential mathematical results devoted to topics of mathematical analysis, differential equations and their various applications. It focuses on differential operators, Wardowski maps, low-oscillation functions, Galois and Pataki connections, Hardy-type inequalities, to name just a few.Effort has been made for this unique title to have an interdisciplinary flavor and features several applications such as in tomography, elastic scattering, fluid mechanics, etc.This work could serve as a useful reference text to benefit professionals, academics and graduate students working in theoretical computer science, computer mathematics, and general applied mathematics.

Multivalued Analysis and Nonlinear Programming Problems with Perturbations

Multivalued Analysis and Nonlinear Programming Problems with Perturbations
Author: B. Luderer
Publisher: Springer Science & Business Media
Total Pages: 218
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475734689

The book presents a treatment of topological and differential properties of multivalued mappings and marginal functions. In addition, applications to sensitivity analysis of nonlinear programming problems under perturbations are studied. Properties of marginal functions associated with optimization problems are analyzed under quite general constraints defined by means of multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the base of the volume. Nonlinear programming problems involving quasidifferentiable functions are considered as well. A significant part of the results are based on theories and concepts of two former Soviet Union researchers, Demyanov and Rubinov, and have never been published in English before. It contains all the necessary information from multivalued analysis and does not require special knowledge, but assumes basic knowledge of calculus at an undergraduate level.

Nonlinear Analysis

Nonlinear Analysis
Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
Total Pages: 898
Release: 2012-06-02
Genre: Mathematics
ISBN: 146143498X

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Author: Mohit Tawarmalani
Publisher: Springer Science & Business Media
Total Pages: 518
Release: 2002-10-31
Genre: Business & Economics
ISBN: 9781402010316

This book provides an insightful and comprehensive treatment of convexification and global optimization of continuous and mixed-integer nonlinear programs. Developed for students, researchers, and practitioners, the book covers theory, algorithms, software, and applications. This thought-provoking book: -develops a powerful and widely-applicable framework for constructing closed-form expressions of convex envelopes of nonlinear functions; -presents a systematic treatment of branch-and-bound, while providing acceleration mechanisms and enhancements; -unifies ideas at the interface between operations research and computer science, devising efficient algorithmic implementation for global optimization; offers students, modelers, and algorithm developers a rich collection of models, applications, and numerical examples; -elucidates through geometric interpretations the concepts discussed throughout the book; -shows how optimization theory can lead to breakthroughs in diverse application areas, including molecular design, process and product design, facility location, and supply chain design and operation; -demonstrates that the BARON software developed by the authors can solve global optimization problems heretofore considered intractable, in an entirely automated manner on a personal computer. Audience: This book will be of interest to researchers in operations research, management science, applied mathematics, computer science, computational chemistry, and all branches of engineering. In addition, the book can be used in graduate level courses in nonlinear optimization, integer programming, global optimization, convex analysis, applied mathematics, and engineering design.