Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of...
Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and ...
Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have...
Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applicati...
At present, concerning intensive development of computer hardware and software, computer-based methods for modeling of difficult problems have become the main technique for theoretical and applied investigations. Many unsolved tasks for evolutionary systems (ES) are an important class of such problems. ES relate to economic systems on the whole and separate branches and businesses, scientific and art centers, ecological systems, populations, separate species of animals and plants, human organisms, different subsystems of organisms, cells of animals and plants, and soon. Available methods for...
At present, concerning intensive development of computer hardware and software, computer-based methods for modeling of difficult problems have become ...
This book provides a new point of view on the field of financial engineering, through the application of multicriteria intelligent decision aiding systems. The aim of the book is to provide a review of the research in the area and to explore the adequacy of the tools and systems developed according to this innovative approach in addressing complex financial decision problems, encountered within the field of financial engineering. Audience: Researchers and professionals such as financial managers, financial engineers, investors, operations research specialists, computer...
This book provides a new point of view on the field of financial engineering, through the application of multicriteria intelligent decision aiding sys...
This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problern with macrovariables, whose number is less than the number of initial variables. This problern is often very simple....
This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by part...
This book shows how the Bayesian Approach (BA) improves well- known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor- tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan- guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for...
This book shows how the Bayesian Approach (BA) improves well- known heuristics by randomizing and optimizing their parameters. That is the Bayesian He...
Fuzzy theory is an interesting name for a method that has been highly effective in a wide variety of significant, real-world applications. A few examples make this readily apparent. As the result of a faulty design the method of computer-programmed trading, the biggest stock market crash in history was triggered by a small fraction of a percent change in the interest rate in a Western European country. A fuzzy theory ap- proach would have weighed a number of relevant variables and the ranges of values for each of these variables. Another example, which is rather simple but pervasive, is that...
Fuzzy theory is an interesting name for a method that has been highly effective in a wide variety of significant, real-world applications. A few examp...
Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to...
Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry a...
Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a mini- mum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that...
Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constraine...
This is a book on Linear-Fractional Programming (here and in what follows we will refer to it as "LFP"). The field of LFP, largely developed by Hungarian mathematician B. Martos and his associates in the 1960's, is concerned with problems of op- timization. LFP problems deal with determining the best possible allo- cation of available resources to meet certain specifications. In particular, they may deal with situations where a number of resources, such as people, materials, machines, and land, are available and are to be combined to yield several products. In linear-fractional programming,...
This is a book on Linear-Fractional Programming (here and in what follows we will refer to it as "LFP"). The field of LFP, largely developed by Hungar...
