Bøger i Applied Optimization serien

However, the modeling and control of technology lifetime under technical change has received rather little attention in mathematical economics in con trary to other aspects of technical progress.

At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems.

Optimization from Human Genes to Cutting Edge Technologies The challenges faced by industry today are so complex that they can only be solved through the help and participation of optimization ex perts.

In this work we are proposing something a little more modest: to use, in the best possible way, data and information that are available for drawing up and applying techniques and instruments that are useful for current reality within the world of businesses and institutions, in an attempt to mislead ourselves as little as possible.

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 Pnkopa started to lay the foundation of a scientific forum, which can be a regular meeting spot for experts of the world in the field.

February 27 - March 1, 1997, the conference Optimal Control: The ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization.

This book presents a unified optimal control approach to a large class of problems arising in the field of production planning and scheduling. This book also introduces the reader to analytical and numerical methods of the maximum principle, used here as a mathematical instrument in modeling and solving production planning and scheduling problems.

This book provides a new point of view on the subject of the management of uncertainty. It covers a wide variety of both theoretical and practical issues involving the analysis and management of uncertainty in the fields of finance, management and marketing.

Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis.

The global market and competition play a crucial part in the decision making processes within the Space and Air industries and this book gives practical examples of how advanced applications can be used by Space and Air industry management.

This book provides a new point of view on the field of financial engineering, through the application of multicriteria intelligent decision aiding systems.

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.

This book shows how the Bayesian Approach (BA) improves well known heuristics by randomizing and optimizing their parameters. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob lems.

This book Algebraic Modeling Systems - Modeling and Solving Real World Optimization Problems - deals with the aspects of modeling and solving real-world optimization problems in a unique combination.

Transportation problems belong to the domains mathematical program ming and operations research. Numerous concrete problems (for example, assignment and distribution problems, maximum-flow problem, etc. In this problem, supply and demand points are given, and it is required to minimize the transportation cost.

Since the book addresses the theory and design of computer-based scheduling algorithms, applied mathematicians and computer software specialists engaged in developing scheduling software for industrial engineering and management problems will find that the methods developed here can be embedded very efficiently in large applications.

This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G.

This volume is an interdisciplinary book which introduces, in a very readable way, state-of-the-art research in the fundamental topics of mathematical modelling of Biosystems. In short, the book offers an overview of mathematical and computational modelling of biosystems including biological phenomena in general.

Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Primary Audience for the Book * Specialists in numerical computations who are interested in algorithms with automatic result verification. * Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc- cessful applications. * Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli- cations of numerical methods with automatic result verification, that were pre- sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.

About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu- tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi- nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi- hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "e;The use of band matrices for second derivative approximations in trust region methods"e;. 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "e;Primal-dual methods for nonconvex optimization"e; by M. H. Wright (SIAM President, Bell Labs), "e;Interior point trajectories in semidefinite programming"e; by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe- matical Programming), "e;An approach to derivative free optimization"e; by A.

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 of an electronic thermostat that turns on heat or air conditioning at a specific temperature setting. In fact, actual comfort level involves other variables such as humidity and the location of the sun with respect to windows in a home, among others. Because of its great applied significance, fuzzy theory has generated widespread activity internationally. In fact, institutions devoted to research in this area have come into being. As the above examples suggest, Fuzzy Systems Theory is of fundamen- tal importance for the analysis and design of a wide variety of dynamic systems. This clearly manifests the fundamental importance of time con- siderations in the Fuzzy Systems design approach in dynamic systems. This textbook by Prof. Dr. Jernej Virant provides what is evidently a uniquely significant and comprehensive treatment of this subject on the international scene.

Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.

Computer-based mathematical modeling - the technique of representing and managing models in machine-readable form - is still in its infancy despite the many powerful mathematical software packages already available which can solve astonishingly complex and large models. On the one hand, using mathematical and logical notation, we can formulate models which cannot be solved by any computer in reasonable time - or which cannot even be solved by any method. On the other hand, we can solve certain classes of much larger models than we can practically handle and manipulate without heavy programming. This is especially true in operations research where it is common to solve models with many thousands of variables. Even today, there are no general modeling tools that accompany the whole modeling process from start to finish, that is to say, from model creation to report writing. This book proposes a framework for computer-based modeling. More precisely, it puts forward a modeling language as a kernel representation for mathematical models. It presents a general specification for modeling tools. The book does not expose any solution methods or algorithms which may be useful in solving models, neither is it a treatise on how to build them. No help is intended here for the modeler by giving practical modeling exercises, although several models will be presented in order to illustrate the framework. Nevertheless, a short introduction to the modeling process is given in order to expound the necessary background for the proposed modeling framework.

The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail.

grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro­ grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C­ programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com­ positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.

The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, `total convexity', is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of Lp. All the material is either new or very recent, and has never been organized in a book. Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc.