Errata and Opinion to:

Errata and Opinion to: “AnInterval Entropy Penalty Method for Nonlinear Global Optimization,” by Zhenyu Huang, Reliable Computing 4 (1) (1998) R. BAKER KEARFOTT Department of Mathematics, University of Louisiana at Lafayette Box 4–1010, Lafayette, LA 70504–1010, USA, e-mail: rbk@louisiana.edu There is an error in this paper which should be corrected, and there is an ambiguous point which should also perhaps be clarified. 1. The Error On the top of page 17, it is stated that: max{ƒ (x),…, ƒ (x)} +max{g (x),…, g (x)} 1 n 1 m =max{ƒ (x)+ g (x),ƒ (x)+ g (x),…, ƒ (x)+ g (x),…, ƒ (x)+ g (x)}. 1 1 1 2 2 1 n m This is well-known to not be true. For example, take m =1, take ƒ(x)= −x ,and take g(x)= −(x − 1) .Then max{ƒ} occurs at x =0, and is equal to 0, while max{g} =0 and occurs at x =1.In contrast max{ƒ + g} = −1 / 2, and it occurs at x =1 / 2. The problem is related to the classical “interval dependency” problem in interval arithmetic. Thecorrect statement is: max{ƒ (x),…, ƒ (x)} +max{g (x),…, g (x)} 1 m 1 m ≤ max{ƒ (x)+ g (x),…, ƒ (x)+ g (x)}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Errata and Opinion to:

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
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.
10.1007/s11155-005-3035-3
Publisher site
See Article on Publisher Site

Abstract

“AnInterval Entropy Penalty Method for Nonlinear Global Optimization,” by Zhenyu Huang, Reliable Computing 4 (1) (1998) R. BAKER KEARFOTT Department of Mathematics, University of Louisiana at Lafayette Box 4–1010, Lafayette, LA 70504–1010, USA, e-mail: rbk@louisiana.edu There is an error in this paper which should be corrected, and there is an ambiguous point which should also perhaps be clarified. 1. The Error On the top of page 17, it is stated that: max{ƒ (x),…, ƒ (x)} +max{g (x),…, g (x)} 1 n 1 m =max{ƒ (x)+ g (x),ƒ (x)+ g (x),…, ƒ (x)+ g (x),…, ƒ (x)+ g (x)}. 1 1 1 2 2 1 n m This is well-known to not be true. For example, take m =1, take ƒ(x)= −x ,and take g(x)= −(x − 1) .Then max{ƒ} occurs at x =0, and is equal to 0, while max{g} =0 and occurs at x =1.In contrast max{ƒ + g} = −1 / 2, and it occurs at x =1 / 2. The problem is related to the classical “interval dependency” problem in interval arithmetic. Thecorrect statement is: max{ƒ (x),…, ƒ (x)} +max{g (x),…, g (x)} 1 m 1 m ≤ max{ƒ (x)+ g (x),…, ƒ (x)+ g (x)}.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

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