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A new three‐point approximation approach for design optimization problems
Author(s) -
Guo Xu,
Yamazaki Koetsu,
Cheng Geng Dong
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010210)50:4<869::aid-nme56>3.0.co;2-c
Subject(s) - taylor series , diagonal , mathematics , reciprocal , expression (computer science) , constraint (computer aided design) , point (geometry) , linear approximation , mathematical optimization , scheme (mathematics) , inverse , function (biology) , mathematical analysis , computer science , geometry , nonlinear system , philosophy , linguistics , physics , quantum mechanics , evolutionary biology , biology , programming language
In this paper, a newly developed three‐point approximation scheme is proposed. The expression of this scheme consists of a linear combination of the direct and reciprocal linear Taylor expansions as well as of the lumped diagonal terms of the second‐order direct and inverse terms. The unknown parameters of the expression are computed on the basis of the function and gradient values at three points in the design space. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of the previously published work. Copyright © 2001 John Wiley & Sons, Ltd.