Chemical Engineering Hand Written_Notes_Part_105

Chemical Engineering Hand Written_Notes_Part_105 - 212 5...

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212 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 A numerical approach to the above one dimensional minimization problem is given in the Appendix. Alternate criteria which can be used for termination of iterations are as follows ¯ ¯ Φ ( z ( k +1) ) Φ ( z ( k ) ) ¯ ¯ | Φ ( z ( k +1) ) | ε Maz i ¯ ¯ ¯ ¯ Φ ( z ( k +1) ) ∂z i ¯ ¯ ¯ ¯ ε ° ° z ( k +1) z ( k ) ° ° ε The Method of steepest descent may appear to be the best unconstrained min- imization method. However due to the fact that steepest descent is a local property, this method is not e f ective in many problems. If the objective func- tion are distorted, then the method can be hopelessly slow. 9.3. Method of Conjugate Gradients. Convergence characteristics of steepest descent can be greatly improved by modifying it into a conjugate gradient method. Method of conjugate gradients display positive characteris-
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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_105 - 212 5...

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