In a mathematical programming problem, an optimum (maxi­ mum or minimum) of a function is sought, subject to con­ straints on the values of the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation - but various other problems, such as the optimal control of an interplanetary rocket, are of similar kind. Often the problems involve nonlinear func­ tions, and so need methods more general than linear pro­ gramming. This book presents a unified theory of nonlinear mathe­ matical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e. g. a continuous curve (i. e. infinitely many variables).

The various methods of linear programming described in this book assume a knowledge of school mathematics but are developed from typical indus- trial problems. I have attempted to use examples to show how practical complications can be introduced into the standard routines. Some of the cases that are described were chosen from less well known fields of appli- cation.

The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.

The book addresses optimization in the petroleum industry from a practical, large-scale-application-oriented point of view. The models and techniques presented help to optimize the limited resources in the industry in order to maximize economic benefits, ensure operational safety, and reduce environmental impact. The book discusses several important real-life applications of optimization in the petroleum industry, ranging from the scheduling of personnel time to the blending of gasoline. It covers a wide spectrum of relevant activities, including drilling, producing, maintenance, and distribution. The text begins with an introductory overview of the petroleum industry and then of optimization models and techniques. The main body of the book details a variety of applications of optimization models and techniques within the petroleum industry.

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research.

Though the volume covers 22 papers by 36 authors from 12 countries, the history in the background is bound to Hungary where, in 1973 Andras Pn§kopa started to lay the foundation of a scientific forum, which can be a regular meeting spot for experts of the world in the field. Since then, there has been a constant interest in that forum.

This book presents novel and original metaheuristics developed to solve the cost-balanced traveling salesman problem. This problem was taken into account for the Metaheuristics Competition proposed in MESS 2018, Metaheuristics Summer School, and the top 4 methodologies ranked are included in the book, together with a brief introduction to the traveling salesman problem and all its variants.

This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined.

This book summarizes years of research in the field of fuzzy relational programming, with a special emphasis on geometric models. It discusses the state-of-the-art in fuzzy relational geometric problems, together with key open issues that must be resolved to achieve a more efficient application of this method. Though chiefly based on research conducted by the authors, who were the first to introduce fuzzy geometric problems, it also covers important findings obtained in the field of linear and non-linear programming. Thanks to its balance of basic and advanced concepts, and its wealth of practical examples, the book offers a valuable guide for both newcomers and experienced researcher in the fields of soft computing and mathematical optimization.