This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Its full treatment ranges from smooth to nonsmooth functions, from convex to nonconvex variational problems, and from economics to mechanics. 1984 edition.
This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Its full trea...
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in...
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of...
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible it has made a subject which is generally inhospitable to nonspecialists because of its family jargon appear nonintimidating even to a beginning graduate student."
The Journal of the Indian Institute of Science
"The book under review gives a comprehensive...
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by h...
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory,...
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions gov...
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning...
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Profe...
Written by seven of the most prominent pioneers of the interval market model and game-theoretic approach to finance, this book provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics."
Written by seven of the most prominent pioneers of the interval market model and game-theoretic approach to finance, this book provides a detailed acc...
This authored monograph presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viability theory and applies this theory to analyze how an economy should be dynamically endowed so that it is economically viable. Economic viability requires an assumption on the joint evolution of transactions, fluctuations of prices and units of numeraire goods: the sum of the transactions values and the impact of price fluctuations should be negative or equal to zero. The book presents a computation of the minimum endowment which restores economic...
This authored monograph presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viabilit...
The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.
These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth. However, shapes and images are basically sets, most often not smooth. J.-P. Aubin...
The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimi...
This authored monograph covers a viability to approach to traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;. It presents an investigation of three structural innovations: The objective is to broadcast at each instant and at each position the advised celerity to vehicles, which could be read by auxiliary speedometers or used by cruise control devices. Namely, 1. Construct regulation feedback providing at each time and position advised velocities (celerities) for minimizing congestion or...
This authored monograph covers a viability to approach to traffic management by advising to vehicles circulated on the network the velocity they sh...
![Set-Valued Analysis Jean-Pierre Aubin Ha(c)La]ne Frankowska 9780817648473 Birkhauser Boston](/9780817648473_set_valued_analysis.jpg "Set-Valued Analysis")
