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Engineering Optimization: Applications, Methods, and Analysis

By
R. Russell Rhinehart
R. Russell Rhinehart
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ISBN:
9781118936337
No. of Pages:
770
Publisher:
ASME Press
Publication date:
2018

Features of a particular application (constraints, inflections, steep valleys) provide difficulty for SQ and NR, which are second-order model-based optimizers. This chapter covers several solutions that typify a myriad of similar adaptations of the basic incremental steepest descent and Newton-type approaches. The topics of this chapter are Levenberg–Marquardt (LM), conjugate gradient (CG), Broyden–Fletcher–Goldfarb–Shanno (BFGS), and generalized reduced gradient (GRG). LM blends ISD and NR to ensure it moves downhill, not to a saddle, maximum, or jump to absurd locations. CG and BFGS are for unconstrained applications with CG being a variant of Cauchy’s sequential line search method and BFGS a quasi-Newton approach. GRG is for handling constraints.

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