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By Sanjay Sharma
Sharma S. utilized Nonlinear Programming (New Age foreign (P) Ltd, 2006)(ISBN 812241771X)
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Step 2 – iff(xL) < f(xR), X1 = xL and M = X2 – X1 xL = previous xR and xR = X1 + Mr Go to step 1. Step 3 – If f(xL) > f(xR), X2 = xR and M = X2 – X1 xR = previous xL and xL = X1 + Mr2 Go to step 1. The procedure is stopped if value of M is considerably small. 4. 1 in which f(x) = 4x – 8x2, is maximized. Implement the method of golden section. 5] in which optimum lies. Solution. 47 As the condition f(xL) > f(xR) is satisfied step 3 is applicable. 47 As f(xL) < f(xR), step 2 is applicable. 24 26 APPLIED NONLINEAR PROGRAMMING It may be observed that only one value out of xL and xR is really changing in each iteration.
1, 1 and –1 respectively in the first, second and third component of the function f. 1 OP −1 Q −1 0. 75 OP N 0. 096 Q N 0. 4 Q N 0. 03 Now M2* = 63158 x2* = w2 . 6 = w3 . f * = 215. 2. 1, a problem concerning fabrication of a cylindrical box is discussed with the objective of minimizing total relevant cost, which is the sum of transportation and fabrication cost. F. 4). This is as followsf (r, h) = 200 πr 2 + 460 πrh + 360 −2 −1 r h π Apply the geometric programming. Solution. F. 554 m f * = Rs.
A1 N wN ( x2* )a21w1 + a22w2 + ... + a2 NwN ... ( xn* )an1w1 + an2w2 + ... + anNwN L ∑ L L C O LC O C O M (x ) = M P M P ... 10), f * LC O = M P Nw Q LC O = M P Nw Q 1 w1 or f * 1 1 LM C OP Nw Q LM C OP Nw Q w1 1 2 w2 2 2 L C OP ... M Nw Q L C OP ... 12) N In order to minimize any posynomial function, w1, w2, ... 10). 12) to get optimum function value f *. xn* are computed. , optimum function value is computed. While in the geometric programming, the reverse takes place. After geting the optimum function value, variables are evaluated.