Online Optimization of Large Scale Systems
Online Optimization of Large Scale Systems

Author: Martin Grötschel

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 789

ISBN-13: 3662043319

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In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.

Advances in Sensitivity Analysis and Parametric Programming
Advances in Sensitivity Analysis and Parametric Programming

Author: Tomas Gal

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 595

ISBN-13: 1461561035

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The standard view of Operations Research/Management Science (OR/MS) dichotomizes the field into deterministic and probabilistic (nondeterministic, stochastic) subfields. This division can be seen by reading the contents page of just about any OR/MS textbook. The mathematical models that help to define OR/MS are usually presented in terms of one subfield or the other. This separation comes about somewhat artificially: academic courses are conveniently subdivided with respect to prerequisites; an initial overview of OR/MS can be presented without requiring knowledge of probability and statistics; text books are conveniently divided into two related semester courses, with deterministic models coming first; academics tend to specialize in one subfield or the other; and practitioners also tend to be expert in a single subfield. But, no matter who is involved in an OR/MS modeling situation (deterministic or probabilistic - academic or practitioner), it is clear that a proper and correct treatment of any problem situation is accomplished only when the analysis cuts across this dichotomy.

Nonlinear Programming
Nonlinear Programming

Author: Anthony V. Fiacco

Publisher: SIAM

Published: 1990-01-01

Total Pages: 226

ISBN-13: 9781611971316

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Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them.

Global Sensitivity Analysis
Global Sensitivity Analysis

Author: Andrea Saltelli

Publisher: John Wiley & Sons

Published: 2008-02-28

Total Pages: 304

ISBN-13: 9780470725177

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Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard. Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications. The book: Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials. Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls. Features numerous exercises and solved problems to help illustrate the applications. Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds. Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.

Operations Research Proceedings 2017
Operations Research Proceedings 2017

Author: Natalia Kliewer

Publisher: Springer

Published: 2018-05-25

Total Pages: 698

ISBN-13: 3319899201

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This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2017), which was held at Freie Universität Berlin, Germany on September 6-8, 2017. More than 800 scientists, practitioners and students from mathematics, computer science, business/economics and related fields attended the conference and presented more than 500 papers in parallel topic streams, as well as special award sessions. The main theme of the conference and its proceedings was "Decision Analytics for the Digital Economy."

Computational Mathematical Programming
Computational Mathematical Programming

Author: Klaus Schittkowski

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 455

ISBN-13: 3642824501

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This book contains the written versions of main lectures presented at the Advanced Study Institute (ASI) on Computational Mathematical Programming, which was held in Bad Windsheim, Germany F. R., from July 23 to August 2, 1984, under the sponsorship of NATO. The ASI was organized by the Committee on Algorithms (COAL) of the Mathematical Programming Society. Co-directors were Karla Hoffmann (National Bureau of Standards, Washington, U.S.A.) and Jan Teigen (Rabobank Nederland, Zeist, The Netherlands). Ninety participants coming from about 20 different countries attended the ASI and contributed their efforts to achieve a highly interesting and stimulating meeting. Since 1947 when the first linear programming technique was developed, the importance of optimization models and their mathematical solution methods has steadily increased, and now plays a leading role in applied research areas. The basic idea of optimization theory is to minimize (or maximize) a function of several variables subject to certain restrictions. This general mathematical concept covers a broad class of possible practical applications arising in mechanical, electrical, or chemical engineering, physics, economics, medicine, biology, etc. There are both industrial applications (e.g. design of mechanical structures, production plans) and applications in the natural, engineering, and social sciences (e.g. chemical equilibrium problems, christollography problems).

Parametric Sensitivity in Chemical Systems
Parametric Sensitivity in Chemical Systems

Author: Arvind Varma

Publisher: Cambridge University Press

Published: 1999-03-13

Total Pages: 361

ISBN-13: 0521621712

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The behavior of a chemical system is affected by many physicochemical parameters. The sensitivity of the system's behavior to changes in parameters is known as parametric sensitivity. When a system operates in a parametrically sensitive region, its performance becomes unreliable and changes sharply with small variations in parameters. Thus, it would be of great value to predict sensitivity behavior in chemical systems. This book is the first to provide a thorough treatment of the concept of parametric sensitivity and the mathematical tool it generated, sensitivity analysis. The emphasis is on applications to real situations. The book begins with definitions of various sensitivity indices and describes the numerical techniques used for their evaluation. Extensively illustrated chapters discuss sensitivity analysis in a variety of chemical reactors - batch, tubular, continuous-flow, fixed-bed - and in combustion systems, air pollution, and metabolic processes. Chemical engineers, chemists, graduate students, and researchers will welcome this valuable resource.

Sensitivity Analysis in Practice
Sensitivity Analysis in Practice

Author: Andrea Saltelli

Publisher: John Wiley & Sons

Published: 2004-07-16

Total Pages: 232

ISBN-13: 047087094X

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Sensitivity analysis should be considered a pre-requisite for statistical model building in any scientific discipline where modelling takes place. For a non-expert, choosing the method of analysis for their model is complex, and depends on a number of factors. This book guides the non-expert through their problem in order to enable them to choose and apply the most appropriate method. It offers a review of the state-of-the-art in sensitivity analysis, and is suitable for a wide range of practitioners. It is focussed on the use of SIMLAB – a widely distributed freely-available sensitivity analysis software package developed by the authors – for solving problems in sensitivity analysis of statistical models. Other key features: Provides an accessible overview of the current most widely used methods for sensitivity analysis. Opens with a detailed worked example to explain the motivation behind the book. Includes a range of examples to help illustrate the concepts discussed. Focuses on implementation of the methods in the software SIMLAB - a freely-available sensitivity analysis software package developed by the authors. Contains a large number of references to sources for further reading. Authored by the leading authorities on sensitivity analysis.