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Unformatted text preview: (9.18) k ( z ) k [ ( z )] T z k ( z ) k and minimum value [ ( z )] T z can attain when z is restricted within the unit ball equals k ( z ) k . In fact, the equality will hold if and only if z is colinear with ( z ) , i.e. (9.19) b z = ( z ) k ( z ) k Thus, unit direction b z given by the above equation is the direction of steepest or maximum descent in which ( z + z ) ( z ) reduces at the maximum rate. Algorithm Given a point z ( z ) , the steepest descent method performs a line search in the direction of ( z ) k ( z ) k , i.e. the direction of steepest descent. INITIALIZE: z (0) , , k max , (0) k = 0 = 100 WHILE [( > ) AND ( k < k max )] s ( k ) = ( z ( k ) ) k ( z ( k ) ) k...
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 Fall '11
 Mr.Shaw
 Chemical Engineering, Optimization

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