Minimax Algebra

Minimax Algebra
Author: R. A. Cuninghame-Green
Publisher: Springer Science & Business Media
Total Pages: 273
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642487084

A number of different problems of interest to the operational researcher and the mathematical economist - for example, certain problems of optimization on graphs and networks, of machine-scheduling, of convex analysis and of approx imation theory - can be formulated in a convenient way using the algebraic structure (R,$,@) where we may think of R as the (extended) real-number system with the binary combining operations x$y, x®y defined to be max(x,y),(x+y) respectively. The use of this algebraic structure gives these problems the character of problems of linear algebra, or linear operator theory. This fact hB.s been independently discovered by a number of people working in various fields and in different notations, and the starting-point for the present Lecture Notes was the writer's persuasion that the time had arrived to present a unified account of the algebra of linear transformations of spaces of n-tuples over (R,$,®),to demonstrate its relevance to operational research and to give solutions to the standard linear-algebraic problems which arise - e.g. the solution of linear equations exactly or approximately, the eigenvector eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.

Minimax and Applications

Minimax and Applications
Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
Total Pages: 300
Release: 2013-12-01
Genre: Computers
ISBN: 1461335574

Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.

Introduction to Lattice Algebra

Introduction to Lattice Algebra
Author: Gerhard X. Ritter
Publisher: CRC Press
Total Pages: 292
Release: 2021-08-23
Genre: Mathematics
ISBN: 1000412601

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises.

Introduction to Minimax

Introduction to Minimax
Author: V. F. Dem’yanov
Publisher: Courier Corporation
Total Pages: 324
Release: 1990-01-01
Genre: Mathematics
ISBN: 0486664236

Geared toward students of mathematical programming, this user-friendly text offers a thorough introduction to the part of optimization theory that lies between approximation theory and mathematical programming. 37 illustrations. 1974 edition.

Linear Algebra

Linear Algebra
Author: Hassan Yasser
Publisher: BoD – Books on Demand
Total Pages: 265
Release: 2012-07-11
Genre: Mathematics
ISBN: 9535106694

Linear algebra occupies a central place in modern mathematics. Also, it is a beautiful and mature field of mathematics, and mathematicians have developed highly effective methods for solving its problems. It is a subject well worth studying for its own sake. This book contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc. It continues to be a definitive resource for researchers, scientists and graduate students.

Surveys in Contemporary Mathematics

Surveys in Contemporary Mathematics
Author: Nicholas Young
Publisher: Cambridge University Press
Total Pages: 370
Release: 2008
Genre: Education
ISBN: 0521705649

A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences
Author: K. Glazek
Publisher: Springer Science & Business Media
Total Pages: 394
Release: 2013-06-29
Genre: Mathematics
ISBN: 9401599645

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Fourth European Symposium on Computer Aided Process Engineering, ESCAPE 4

Fourth European Symposium on Computer Aided Process Engineering, ESCAPE 4
Author: F. A. Perris
Publisher: IChemE
Total Pages: 544
Release: 1994
Genre: Chemical engineering
ISBN: 9780852953211

The ESCAPE symposia address the applications of computer aids to all aspects of process engineering. The primary objective is the interchange of information on industrial needs, new technology developments and research opportunities. With industrialists and academia contibuting from all over the world, this set of proceedings provides an overview of current international computer-aided process engineering (CAPE). This book is intended for chemical and process engineers, design engineers and computer-aided specialists.