1 edition of **Approximation and complexity in numerical optimization** found in the catalog.

- 140 Want to read
- 31 Currently reading

Published
**2000**
.

Written in English

- Mathematical optimization,
- Approximation theory,
- Computational complexity

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems, from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new approximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization problems, new approximate algorithms have been developed based on semidefinite programming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. The two themes of approximation and complexity pervade this book. Audience: Faculty, graduate students, and researchers in mathematical programming, computer sciences and engineering.

**Edition Notes**

Statement | edited by Panos M. Pardalos, Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, U.S.A. |

Series | Nonconvex optimization and its applications -- volume 42, Nonconvex optimization and its applications -- v. 42. |

Classifications | |
---|---|

LC Classifications | QA402.5 .A66 2000eb |

The Physical Object | |

Pagination | 1 online resource (xvii, 581 pages). |

Number of Pages | 581 |

ID Numbers | |

Open Library | OL27017747M |

ISBN 10 | 1475731450, 1441948295 |

ISBN 10 | 9781475731453, 9781441948298 |

OCLC/WorldCa | 863638125 |

This note covers the following topics: Approximation and Interpolation, Numerical Quadrature, Direct Methods of Numerical Linear Algebra, Numerical solution of nonlinear systems and optimization, Numerical Solution of Ordinary Differential Equations, Numerical Solution of Partial Differential Equations and e Iterative Methods of Numerical. For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods.

This book is addressed to students in the fields of engineering and technology as well as practicing engineers. It covers the fundamentals of commonly used optimization methods in engineering design. These include graphical optimization, linear and nonlinear programming, numerical optimization, and discrete optimization/5(26). Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity.

their complexity analysis. This book is meant to be something in between, a book on general convex optimization that focuses on problem formulation and modeling. We should also mention what this book is not. It is not a text primarily about convex analysis, or the mathematics of convex optimization; several existing texts cover these topics well. This book deals with designing polynomial time approximation algorithms for NP-hard optimization problems. Typically, the decision versions of these problems are in NP, and are therefore NP-complete. From the viewpoint of exact solutions, all NP-complete problems are equally hard, since they are inter-reducible via polynomial time reductions.

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A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, at the Center for Applied Optimization of the University of Florida.

A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, at the Center for Applied Optimization of the University of : Hardcover.

The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.

Contents. Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems.

Get this from a library. Approximation and complexity in numerical optimization book and complexity in numerical optimization: continuous and discrete problems. [P M Pardalos;]. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, at the Center for Applied Optimization of the University of Florida.

The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network.

We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense.

In formal terms, they are classified as Np-hard optimization problems. This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization.

Approximation-And-Complexity-In-Numerical-Optimization-Continuous-And-Discrete-Sm Adobe Acrobat Reader DCDownload Adobe Acrobat Reader DC Ebook PDF:With Acrobat Reader DC you can do more than just open and view PDF files Its easy to add annotations to documents using a complete set of commenting tools Take your PDF tools to.

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine.

Publisher Summary. This chapter presents an introduction to this book. The book is structured into three parts. The first part, “Fundamentals,” begins with an introduction to numerical analysis, so one discusses computer arithmetic, approximation errors, how to solve linear equations, how to approximate derivatives, and other topics.

Numerical complexity is defined here as the number of floating point operations required to execute an algorithm (flops). A flop corresponds to a multiplication followed by an addition. But, in practice, only the number of multiplications is considered since, most of the time, there are about as many (and slightly more) multiplications as.

Numerical Complex Analysis. This note covers the following topics: Fourier Analysis, Least Squares, Normwise Convergence, The Discrete Fourier Transform, The Fast Fourier Transform, Taylor Series, Contour integration, Laurent series, Chebyshev series, Signal smoothing and root finding, Differentiation and integration, Spectral methods, Ultraspherical spectral methods.

Approximation structures with moderate complexity in functional optimization and dynamic programming Conference Paper December with 35 Reads How we measure 'reads'. Convex Optimization: Algorithms and Complexity by Sebastien Bubeck -This text presents the main complexity theorems in convex optimization and their algorithms.

Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural and stochastic optimization. Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties - Ebook written by Giorgio Ausiello, Pierluigi Crescenzi, Giorgio Gambosi, Viggo Kann, Alberto Marchetti-Spaccamela, Marco Protasi.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, Author: Giorgio Ausiello. A conference on Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems was held during February 28 to March 2, at the Center for Applied Optimization of the University of Florida.

Mathematical optimization (alternatively spelt optimisation) or mathematical programming is the selection of a best element (with regard to some criterion) from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods.

These are the questions that complexity theory attempts to address. The theory originated in work by Hartmanis and Stearns (). By now there is much known about complexity issues in nonlinear optimization. In particular, our recent book Vavasis () contains all the details on many of the results surveyed in this chapter.

Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional settings, involving for instance several .Book Description.

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods.Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more.

"Mathematicians wishing a self-contained introduction need look no further.".