Semi-Infinite Fractional Programming
Semi-Infinite Fractional Programming

Author: Ram U. Verma

Publisher: Springer

Published: 2017-10-24

Total Pages: 298

ISBN-13: 9811062560

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This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.

Linear Semi-Infinite Optimization
Linear Semi-Infinite Optimization

Author: Miguel A. Goberna

Publisher:

Published: 1998-03-11

Total Pages: 380

ISBN-13:

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A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012
Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012

Author: Zhicai Zhong

Publisher: Springer Science & Business Media

Published: 2013-03-28

Total Pages: 865

ISBN-13: 1447148533

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Information engineering and applications is the field of study concerned with constructing information computing, intelligent systems, mathematical models, numerical solution techniques, and using computers and other electronic devices to analyze and solve natural scientific, social scientific and engineering problems. Information engineering is an important underpinning for techniques used in information and computational science and there are many unresolved problems worth studying. The Proceedings of the 2nd International Conference on Information Engineering and Applications (IEA 2012), which was held in Chongqing, China, from October 26-28, 2012, discusses the most innovative research and developments including technical challenges and social, legal, political, and economic issues. A forum for engineers and scientists in academia, industry, and government, the Proceedings of the 2nd International Conference on Information Engineering and Applications presents ideas, results, works in progress, and experience in all aspects of information engineering and applications.

Advances in Computer, Communication, Control and Automation
Advances in Computer, Communication, Control and Automation

Author: Yanwen Wu

Publisher: Springer Science & Business Media

Published: 2011-11-20

Total Pages: 786

ISBN-13: 3642255418

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The volume includes a set of selected papers extended and revised from the 2011 International Conference on Computer, Communication, Control and Automation (3CA 2011). 2011 International Conference on Computer, Communication, Control and Automation (3CA 2011) has been held in Zhuhai, China, November 19-20, 2011. This volume topics covered include signal and Image processing, speech and audio Processing, video processing and analysis, artificial intelligence, computing and intelligent systems, machine learning, sensor and neural networks, knowledge discovery and data mining, fuzzy mathematics and Applications, knowledge-based systems, hybrid systems modeling and design, risk analysis and management, system modeling and simulation. We hope that researchers, graduate students and other interested readers benefit scientifically from the proceedings and also find it stimulating in the process.

Encyclopedia of Optimization
Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Mathematics and Computing
Mathematics and Computing

Author: Ram N. Mohapatra

Publisher: Springer

Published: 2015-06-25

Total Pages: 500

ISBN-13: 8132224523

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This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computing are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. In current research, modeling and simulation, making decisions under uncertainty and pattern recognition have become very common. Professionals across different educational levels and disciplines need exposure to advances in mathematics and computing. In this context, this book presents research papers on applicable areas of current interest. It also includes papers in which experts summarize research findings, such as signal processing and analysis and low-rank-matrix approximation for solving large systems, which will emerge as powerful tools for further research. These new advances and cutting-edge research in the fields of mathematics and their applications to computing are of paramount importance for young researchers.

Handbook of Generalized Convexity and Generalized Monotonicity
Handbook of Generalized Convexity and Generalized Monotonicity

Author: Nicolas Hadjisavvas

Publisher: Springer Science & Business Media

Published: 2006-01-16

Total Pages: 684

ISBN-13: 0387233938

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Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.

Operations Research and Optimization
Operations Research and Optimization

Author: Samarjit Kar

Publisher: Springer

Published: 2018-04-06

Total Pages: 399

ISBN-13: 9811078149

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This book discusses recent developments in the vast domain of optimization. Featuring papers presented at the 1st International Conference on Frontiers in Optimization: Theory and Applications (FOTA 2016), held at the Heritage Institute of Technology, Kolkata, on 24–26 December 2016, it opens new avenues of research in all topics related to optimization, such as linear and nonlinear optimization; combinatorial-, stochastic-, dynamic-, fuzzy-, and uncertain optimization; optimal control theory; as well as multi-objective, evolutionary and convex optimization and their applications in intelligent information and technology, systems science, knowledge management, information and communication, supply chain and inventory control, scheduling, networks, transportation and logistics and finance. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Recent Advances in Nonlinear Analysis and Optimization with Applications
Recent Advances in Nonlinear Analysis and Optimization with Applications

Author: Savin Treanţă

Publisher: Cambridge Scholars Publishing

Published: 2020-09-30

Total Pages: 146

ISBN-13: 1527560384

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This book focuses on recent advances in nonlinear analysis and optimization with important applications drawn from various fields, such as artificial intelligence, genetic algorithms, optimization problems under uncertainty, and fuzzy logic. Specifically, it is devoted to nonlinear problems associated with optimization which have some connection with applications. The ideas and techniques developed here will serve to stimulate further research in this dynamic field, and, in this way, the book will become a valuable reference for researchers, engineers and students in the field of mathematics, management science, operations research, optimal control science and economics.

Completely Positive Matrices
Completely Positive Matrices

Author: Abraham Berman

Publisher: World Scientific

Published: 2003

Total Pages: 222

ISBN-13: 9789812795212

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A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."