Topological Aspects of Nonsmooth Optimization, Vladimir Shikhman

Автор: Brown Robert F.
Название: A Topological Introduction to Nonlinear Analysis
ISBN: 0817632581 ISBN-13(EAN): 9780817632588
Издательство: Springer
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Описание: "The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise." —MATHEMATICAL REVIEWS (Review of the First Edition) Here is a book that will be a joy to the mathematician or graduate student of mathematics---or even the well-prepared undergraduate---who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world.New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book. * Several new proofs, making the second edition more self-contained.

Автор: V. Jeyakumar; Dinh The Luc
Название: Nonsmooth Vector Functions and Continuous Optimization
ISBN: 1441944729 ISBN-13(EAN): 9781441944726
Издательство: Springer
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Описание: Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions.

Автор: Leger Alain
Название: Qualitative Analysis of Nonsmooth Dynamics
ISBN: 1785480944 ISBN-13(EAN): 9781785480942
Издательство: Elsevier Science
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Описание:

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses.

Автор: Vincent Acary; Bernard Brogliato
Название: Numerical Methods for Nonsmooth Dynamical Systems
ISBN: 3642094643 ISBN-13(EAN): 9783642094644
Издательство: Springer
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Описание: This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses.

Автор: Pierre Alart; Olivier Maisonneuve; R. Tyrrell Rock
Название: Nonsmooth Mechanics and Analysis
ISBN: 1441939768 ISBN-13(EAN): 9781441939760
Издательство: Springer
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Описание: Convex and Nonsmooth Analysis.- Moreau's Proximal Mappings and Convexity in Hamilton-Jacobi Theory.- Three Optimization Problems in Mass Transportation Theory.- Some Geometrical and Algebraic Properties of Various Types of Convex Hulls.- A Note on the Legendre-Fenchel Transform of Convex Composite Functions.- What Is to be a Mean?.- Nonsmooth Mechanics.- Thermoelastic Contact with Frictional Heating.- A Condition for Statical Admissibility in Unilateral Structural Analysis.- Min-Max Duality and Shakedown Theorems in Plasticity.- Friction and Adhesion.- The Clausius-Duhem Inequality, an Interesting and Productive Inequality.- Unilateral Crack Identification.- Penalty Approximation of Painlevй Problem.- Discrete Contact Problems with Friction: A Stress-Based Approach.- Fluid Mechanics.- A Brief History of Drop Formation.- Semiclassical Approach of the "Tetrad Model" of Turbulence.- Multibody Dynamics: Numerical Aspects.- The Geometry Of Newton's Cradle.- Using Nonsmooth Analysis for Numerical Simulation of Contact Mechanics.- Numerical Simulation of a Multibody Gas.- Granular Media and Ballasted Railway Tracks Milieux Granulaires Et Voies Ballastйes.- Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows.- Topics in Nonsmooth Science.- Morphological Equations and Sweeping Processes.- Higher Order Moreau's Sweeping Process.- An Existence Result in Non-Smooth Dynamics.- Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction.- Canonical Duality in Nonsmooth, Constrained Concave Minimization.

Автор: Messaoud Bounkhel
Название: Regularity Concepts in Nonsmooth Analysis
ISBN: 1489989374 ISBN-13(EAN): 9781489989376
Издательство: Springer
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Описание: The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis.