Task 16
Find minimum of the function
f = 1,5x12 - 6x22 - 2,5x32 + 4x42 + 3x52 - 4x1x2 + 8x1x3 + 4x1x4 + 3x1x5 + x2x3 + 6x2x4 - 6x2x5 + 6x3x4 - 4x3x5 + 2x4x5 + 8x1 + 5x2 + 12x3 + 10x4 + 6x5
subject to
2x1 + x2 + 4x3 - 4x4 + 2x5 < 40
6x1 + 10x2 + 2x3 - 12x4 + 16x5 < 30
6x1 + 3x2 + 12x3 + 6x4 + 8x5 < 36
4x1 + 8x2 + 12x3 - 12x4 - 2x5 < 70
6x1 + 8x2 + 12x3 + 8x4 + 4x5 < 80

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   1,5   -2   4   2   1,5
  -2   -6   0,5   3   -3
  4   0,5   -2,5   3   -2
  2   3   3   4   1
  1,5   -3   -2   1   3

L =   8  
x1
  5
x2
  12
x3
  10
x4
  6
x5



Outcome

Function is unbounded, for example, on the ray M0 + Vt, t > 0:
  f = at2 + bt + c
  a = -2,07861506758993
  b = -0,820702504892339
  c = 459,889804787467
    M0   V
x1
  18,8068310218842   -1
x2
  -8,12172155538593   0,049680624556423
x3
  0,0751115058976918   0,31582682753726
x4
  -4,27149842768337   -0,0312278211497516
x5
  -3,51373193612687   0,281050390347764

Execution constraints:
Ak - vector coefficients of left side of constraints number "k", Bk - right side of constraints number "k".
  (Ak , M0)     Bk   (Ak ,V)
  39,850916350453
<
  40   0
  26,812263743412
<
  30   -8,88178419700125E-16
  35,6383134808047
<
  36   4,44089209850063E-16
  69,4403347196759
<
  70   1,11022302462516E-16
  0,541636593015806
<
  80   -0,938254080908446
Yellow highlighted lines, that match planes of constraints polyhedron, that are parallel to the ray. In the last column of this row's the number is not zero only due to computational error.
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