Interval Methods for Accelerated Global Search in the Microsoft Excel Solver

Interval Methods for Accelerated Global Search in the Microsoft Excel Solver This paper describes advanced interval methods for finding a global optimum and finding all solutions of a system of nonlinear equations, as implemented in the Premium Solver Platform, an extension of the Solver bundled with Microsoft Excel. It also describes the underlying tools that allow Excel spreadsheets to be evaluated over real and interval numbers, with fast computation of real gradients and interval gradients. The advanced interval methods described include mean value (MV) and generalized interval (GI) representations for functions, constraint propagation for both the MV and GI forms, and a linear programming test for the GI form, in the context of an overall interval branch and bound algorithm. Numerical results for a set of sample problems demonstrate a significant speed advantage for the GI techniques, compared to alternative methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Interval Methods for Accelerated Global Search in the Microsoft Excel Solver

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1023042418784
Publisher site
See Article on Publisher Site

Abstract

This paper describes advanced interval methods for finding a global optimum and finding all solutions of a system of nonlinear equations, as implemented in the Premium Solver Platform, an extension of the Solver bundled with Microsoft Excel. It also describes the underlying tools that allow Excel spreadsheets to be evaluated over real and interval numbers, with fast computation of real gradients and interval gradients. The advanced interval methods described include mean value (MV) and generalized interval (GI) representations for functions, constraint propagation for both the MV and GI forms, and a linear programming test for the GI form, in the context of an overall interval branch and bound algorithm. Numerical results for a set of sample problems demonstrate a significant speed advantage for the GI techniques, compared to alternative methods.

Journal

Reliable ComputingSpringer Journals

Published: Oct 17, 2004

References

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