Author: Kathy A. Lewis
Publisher:
ISBN:
Category :
Languages : en
Pages : 178

View

Book Description

Author: Assem Deif
Publisher: Springer Science & Business Media
ISBN: 364282739X
Category : Technology & Engineering
Languages : en
Pages : 235

View

Book Description
A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.

Author: Aharon Ben-Tal
Publisher: Princeton University Press
ISBN: 1400831059
Category : Mathematics
Languages : en
Pages : 565

View

Book Description
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Author: Miguel A. Goberna
Publisher: Springer Science & Business Media
ISBN: 148998044X
Category : Business & Economics
Languages : en
Pages : 128

View

Book Description
Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

Author: Jiyoung Im
Publisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 97

View

Book Description
In this thesis, we study the special case of linear optimization to show what may affect the sensitivity of the optimal value function under data uncertainty. In this special case, we show that the robust optimization problem with a locally smaller feasible region yields a more conservative robust optimal value than the one with a locally bigger feasible region. To achieve that goal, we use a geometric approach to analyze the sensitivity of the optimal value function for linear programming (LP) under data uncertainty. We construct a family of proper cones where the strict containment holds for any pair of cones in the family. We then form a family of LP problems using this family of cones constructed above; the feasible regions of each pair of LPs in the family holds strict containment, every LP in the family has the unique optimal solution at the vertex of the cone and has the same objective function, i.e., every LP in the family shares the same optimal solution and the same optimal value. We rewrite he LPs so that they reflect the given data uncertainty and perform local analysis near the optimal solutions where the local strict containment holds. Finally, we illustrate that an LP with a locally smaller feasible region is more sensitive than an LP with a locally bigger feasible region.

Author: C. M. Shetty
Publisher:
ISBN:
Category :
Languages : en
Pages :

View

Book Description

Author: Tomas Gal
Publisher: Springer Science & Business Media
ISBN: 1461561035
Category : Business & Economics
Languages : en
Pages : 595

View

Book Description
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.

Author: K. K. Choi
Publisher: Springer Science & Business Media
ISBN: 0387273069
Category : Science
Languages : en
Pages : 336

View

Book Description
Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Author: Wayne L. Winston
Publisher: Duxbury Resource Center
ISBN:
Category : Business & Economics
Languages : en
Pages : 762

View

Book Description
Vol. 2: CD-ROM contains student editions of: ProcessModel, LINGO, Premium Solver, DecisionTools Suite including @RISK AND RISKOptimizer, Data files.

Author: Paul R. Thie
Publisher: John Wiley & Sons
ISBN: 1118165454
Category : Mathematics
Languages : en
Pages : 476

View

Book Description
Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.