Applied Optimization

By: V. Kreinovich, A.V. Lakeyev, J. Rohn

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Hardcover | 31 December 1997

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476 Pages

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25.4 x 17.15 x 3.18

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Targeted audience â¢ Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. â¢ Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. â¢ Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

Industry Reviews

`The book is very well organized. The book is readable, very detailed, and intelligible. Moreover, it is exciting and gripping because the reader is often surprised by unexpected results. Everyone who is interested in modern aspects of numerical computation will enjoy reading this interesting and informative work. The book is a must for everyone who is doing research in this field.'
Mathematical Reviews, 98m

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Non-Fiction Computing & I.T.Computer Science Mathematical Theory of Computation Mathematics Mathematical Foundation Databases Data Capture & Analysis Applied Mathematics Calculus & Mathematical Analysis Numerical Analysis Probability & Statistics

Optimisation

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Published: 10th December 2010

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Preface
Informal Introduction: Data Processing, Interval Computations, and Computational Complexity	p. 1
The Notions of Feasibility and NP-Hardness: Brief Introduction	p. 23
In The General Case, The Basic Problem of Interval Computations is Intractable	p. 41
Basic Problem of Interval Computations for Polynomials of a Fixed Number of Variables	p. 53
Basic Problem of Interval Computations for Polynomials of Fixed Order	p. 71
Basic Problem of Interval Computations for Polynomials with Bounded Coefficients	p. 79
Fixed Data Processing Algorithms, Varying Data: Still NP-Hard	p. 83
Fixed Data, Varying Data Processing Algorithms: Still Intractable	p. 85
What If We Only Allow Some Arithmetic Operations in Data Processing?	p. 87
For Fractionally-Linear Functions, A Feasible Algorithm Solves the Basic Problem of Interval Computations	p. 91
Solving Interval Linear Systems is NP-Hard	p. 99
Interval Linear Systems: Search for Feasible Classes	p. 111
Physical Corollary: Prediction is Not Always Possible, Even for Linear Systems with Known Dynamics	p. 143
Engineering Corollary: Signal Processing is NP-Hard	p. 153
Bright Sides of NP-Hardness of Interval Computations I: NP-Hard Means That Good Interval Heuristics Can Solve Other Hard Problems	p. 159
If Input Intervals are Narrow Enough, Then Interval Computations are Almost Always Easy	p. 161
Optimization - A First Example of a Numerical Problem in Which Interval Methods are Used: Computational Complexity and Feasibility	p. 173
Solving Systems of Equations	p. 197
Approximation of Interval Functions	p. 207
Solving Differential Equations	p. 219
Properties of Interval Matrices I: Main Results	p. 225
Properties of Interval Matrices II: Proofs and Auxiliary Results	p. 257
Non-Interval Uncertainty I: Ellipsoid Uncertainty and Its Generalizations	p. 289
Non-Interval Uncertainty II: Multi-Intervals and Their Generalizations	p. 309
What If Quantities are Discrete?	p. 325
Error Estimation for Indirect Measurements: Interval Computation Problem is (Slightly) Harder than a Similar Probabilistic Computational Problem	p. 331
In Case of Interval (or More General) Uncertainty, No Algorithm Can Choose the Simplest Representative	p. 347
Error Estimation for Indirect Measurements: Case of Approximately Known Functions	p. 365
From Interval Computations to Modal Mathematics	p. 381
Beyond NP: Two Roots Good, One Root Better	p. 395
Does "NP-Hard" Really Mean "Intractable"?	p. 401
Bright Sides of NP-Hardness of Interval Computations II: Freedom of Will?	p. 405
The Worse, The Better: Paradoxical Computational Complexity of Interval Computations and Data Processing	p. 409
References	p. 413
Index	p. 451
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Optimization

At a Glance

Hardcover

Industry Reviews

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You Can Find This Book In

Other Editions and Formats

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