Implement one iteration of the Steepest Descent method with a0) = (0,1,1)* towards ap- proximating the minimum of the function %3D g(*1,#2,3) = 10 (xi – až + 2x2)* + æz² + a %3D
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- Find the optimum of f(x) = 2.2x – 1.7x2 + x3 – 0.25x4 Perform: (Round-off all computed values to 4 decimal places.)a) (2 iterations) Golden-Section Search using XL = –2.4 and XU = 4.5 For each iteration, show the following: d, X1, X2, decision rule, ea, and the next XL andXU Are you approaching a local or global optimum? ____________ Are you approaching a minimum or maximum optimum? __________Consider the LP Problem (attached image): (b) Write down the dual problem and find an optimal solution. Is it unique?a)The formula of calculating an upper bound of theabsolute error in bisection method is stronger thanthose of the fixed point iteration.Select one:TrueFalse b)Let g(x) = x2 – 2x – 4 on [-2, 4] , then the fixedpoints for g(x) are:Select one:a. -1 and 4b.-1C. 4d. -1 and -4 c) The number of iterations necessary to achieve an accuracy 10-2using bisection method on theinterval [0,2] is:Select one:a. 6b. 8c. 7d. 5 d)Secant Method is faster than Newton RaphsonMethod.Select one:a. Yesb. No e) The fractional part (mantissa) of the machinenumber0 01100000111 01010011000 isSelect one:a. 0.32980b. 0.72421875c. 0.32421875d. 0.421875
- Consider the problem (attached image) min x2 subject to x2 = 1 x1, x2 ≥ 0 Write down its dual. For both the primal and the dual problem determine whether they have unique optimal solutions and whether they have nondegeneration optimal solutions.f(x) = 4x - 1.8x2+1.2x3-0.3x4 Find the maximum using Golden-Section search (Xlower = -2, Xupper= 4 with a percentage error 1%) Show the whole solutionThe path of steepest ascent is usually computed assuming that the model is truly first order; that is, there is no interaction. However, even if there is interaction, steepest ascent ignoring the interaction still usually produces good results. To illustrate, suppose that we have fit the model ˆy =20+5x1−8x2+3x1x2ŷ=20+5x1−8x2+3x1x2 Using coded variables (−1 ≤ xi ≤ +1) a) Draw the path of steepest ascent that you would obtain if the interaction were ignored. b) Draw the path of steepest ascent that you would obtain with the interaction included in the model. Compare this with the path found in part (a).