Chemical Engineering Hand Written_Notes_Part_108

Chemical Engineering Hand Written_Notes_Part_108 - 218 5....

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218 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES λ k = min λ Φ ¡ z ( k ) λ s ( k ) ¢ z ( k +1) = z ( k ) λ k s ( k ) δ = ° ° Φ £ z ( k +1) ¤° ° 2 END WHILE 9.4.1. Quasi- Newton Method. Major disadvantage of Newtons method or its variants is the need to compute the Hessian of each iteration . The quasi-Newton methods over come this di cu l tybycon s t ru c t inganapp rox i - mate Hessian from the gradient information available at the successive itera- tion. Quasi-Newton methods thus mimic positive characteristics of Newton’s method using only gradient information. All methods of this class generate search direction as (9.69) s ( k ) = D ( k ) f ( k ) which is similar to the Newton’s update, i.e. s ( k ) = [ H ( k ) ] 1 f ( k ) Here,
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_108 - 218 5....

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