Question

min (x2 - 2 x1)4 + 64 xj x2 XER and the points a = (1,5), b = (0,0)", c= (1,-1)", d= (-3,1) Select all true statements from the options below: TESCO give ... score for this problem may be smaller than the actual one after we added partial credits Od is a global minimizer Othere is only one global minimizer cis a strict local minimizer Od is a strict local minimizer the objective function is coercive Ob is a local minimizer O ais a saddle point

Answer 1

min • 2x + 64 x 22 - XER² min (22-223" + 64*, *2-462) a- (3), de ce ost, cal - ), d-(-3,1) f(x) = (22 - 2879 + buraz - 4(x-243".(2) + Luy .. 4(22-24,3% + bu x : ato -8 (22 - 2x 3 + bu q=0 (22 - 2343-822 = o -o ox &o- here rue e-keng tarber- 0-691+Chur - 22 ©- = 20 8-3x ) ah od te hot sex-2x) ha- - eebee n 2- 22 4 Halsian Matrix oxon 04 any ay ang

(48 (x2 – 2x2 -24 (82 - 2x +by - 2404-22, 2464 12 (22-24) from , & and (3-2-22 2 2-4*-* so a is not saddle point because should be satisfied at a= l, 2) I and @ but not the case H = od and at b= (e, og from ſo 64 1 (HI = – 642 to and prineople diagonal became the is not also non positive s b is not a local minimizer. at - (2, - 13T 192 32 , 140 H = 32 48 C 192 32

because all the values of H are non zen and positive of strictly positive and determinant also positive so H is strictly positive definite so f(x) is strictly minimale at a so c is strictly local minimizer, because and also satisfres at d = ( 2 , 18 from T192 321 - 1 (H12O H = | 32 48 from 8 - 8 = 0 sutisties from @ -8 + 8 so salutis se d also local minimizer because lim feug = to so xello so selected options. & is a strict local minimizer d is a strict local minimizer & the objective function is wescive fry is coercive