In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

Since the turn of the century, geology has advanced dramatically, with materials derived from extra-terrestrial sources meaning that it now encompasses cosmology, and new technologies providing ever more sophisticated possibilities for the conducting of research. This book, Unconventional Methods for Geoscience, Shale Gas and Petroleum in the 21st Century, aims to provide research directions for geology in the 21st century. As Eric Hobsbawm wrote, it is difficult to write the history of one’s own days, and selecting influential methods was no easy task, but an attempt has been made to include the most influential papers that represent the smart geology of the first few decades of the 21st century. The book presents 22 papers; the first serves as an introduction to biology, which is now expanding into the science of the cosmos following the discovery of previously missing information, and the remaining 21 papers are divided into 3 sections entitled Modelling, Simulation and Optimization. The importance of theoretical approaches from physics, mathematics, and statistics underlying meta-heuristic methods, knowledge and approaches is acknowledged, and there is a chapter dedicated to deep learning. The book contributes to the exploration of various possible solutions to challenging problems in both the Earth’s geology and that of the cosmos, and will be of interest to all those working in the field.

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.

This book focuses on the tremendous development that has taken place recently in the field of of nondifferentiable nonconvex optimization. Coverage includes the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the co-derivative of Mordukhovich), the opening of new applications (the calibration of water supply systems), and the elaboration of new solution algorithms (e.g., smoothing methods).

This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.

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.

This extremely useful book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. The text is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.

'Since the extraordinary impact of networks is self-evident today both in the field of telecommunications and transportation as well as in the field of economic and financial equilibria, the scientific work carried out by Patrizia Daniele appears as an outstanding resource. The author employs with uncommon competence mathematical topics that are at the forefront of the science, while at the same time enabling the reader to understand the matter treated without any difficulty. Moreover the reader is fascinated by the clarity, depth and soundness with which the evolutionary equilibria problems are studied and by the original efficient computational procedures which allow for the solving of many significant examples and concrete problems. Without any doubt the book represents a shining light and a necessary tool for scholars of pure and applied mathematics, for economists and engineers as well as for practitioners, general managers and managing directors.' - Antonino Maugeri, Università di Catania, Italy This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of 'dynamic' networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.

The Intelligent Decision Technologies (IDT) International Conference encourages an interchange of research on intelligent systems and intelligent technologies that enhance or improve decision making. The focus of IDT is interdisciplinary and includes research on all aspects of intelligent decision technologies, from fundamental development to real applications. IDT has the potential to expand their support of decision making in such areas as finance, accounting, marketing, healthcare, medical and diagnostic systems, military decisions, production and operation, networks, traffic management, crisis response, human-machine interfaces, financial and stock market monitoring and prediction, and robotics. Intelligent decision systems implement advances in intelligent agents, fuzzy logic, multi-agent systems, artificial neural networks, and genetic algorithms, among others. Emerging areas of active research include virtual decision environments, social networking, 3D human-machine interfaces, cognitive interfaces, collaborative systems, intelligent web mining, e-commerce, e-learning, e-business, bioinformatics, evolvable systems, virtual humans, and designer drugs. This volume contains papers from the Fourth KES International Symposium on Intelligent Decision Technologies (KES IDT’12), hosted by researchers in Nagoya University and other institutions in Japan. This book contains chapters based on papers selected from a large number of submissions for consideration for the conference from the international community. The volume represents the current leading thought in intelligent decision technologies.

This is the second volume of the book series featuring empirical research conducted on business decision making policies of oligopolistic organizations. This volume brings together 11 chapters that cover economic and mathematical models to illustrate strategic decision making among different organizations. Topics covered in this volume include, the theory of firm behavior, the Bertrand model of an incumbent and a potential industrial entrant, strategic interactions in vertically related industries, financial losses of enterprises caused by breaks of information security systems and the association of certain funding choices with efficiency in small medium enterprises. Thus the volume encompasses a fresh collection of works on firm behavior and industrial economics.