In addition to providing correct answers (part B of the question), this question also requires including an additional a

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In Addition To Providing Correct Answers Part B Of The Question This Question Also Requires Including An Additional A 1 (85.31 KiB) Viewed 12 times

In addition to providing correct answers (part B of the question), this question also requires including an additional answer (working out) in a separately submitted document (part A of the question). If the additional answer is not submitted or is significantly incorrect, then the mark of Zero will be given for the whole question, irrespective of the selected quiz answers. Otherwise (that is, if the additional answer is broadly correct), the mark for this question will be the mark obtained for the quiz answers. You should start preparing your answer to part A of the question while you are working on the quiz, because when you submit your quiz, you will no longer have access to the questions. Consider the following minimization problem over x1,x2 € R minimise+ subject to x1 + x2 = 1 (constraint ) xi 01, (constraint 120) x22 0.2 (constraint v220) Part A. Given Lagrange multipliers 1.42, for the inequality constrains, and a multiplier R for equality constraint (nate: please write the equality constraint as x1 + x2-1=0 , NOT 1-x1 - x2 = 0 ) i write down the Lagrangian of the given instance, 10 write down the KKT conditions of the given instance. Part B. Complete the following statements to make them correct. It is that the considered problem is convex It is that the strong duality holds for the considered problem. It is that the variable needs to be negative to make the critical point of the Lagranglan well defined. The critical point for the Lagrangian (where its gradient must vanish) is and where A=²==== Based on KKT conditions, the optimal solution for the primal problem is (x1,x2) and the optimal solution for the dual problem is a n without any constraints. Now consider minimizing the cost function /(x) = + Complete the following statements to make them correct. where The gradient of /ix) is given as - - - ਯਾਦਾ = ਜੱਗਾ ਗੰਦਾ B = = ਜੱਟਾ - ਜੰਮ If we initialise so[1/5, 2/5] and set the step size to be a = 0.01 After one step af gradient descent, x= where E$I=n F咱I = 3 | W响 =« * ¥咱I = v ADCD True False DIADE (1/3, 2/3 (2/3, 1/3, 1/5, 4/5/2/5, 3/5