Task 5
Find minimum of the function
f = x12 - 15x22 + 50x1x2 - 12x1x3 + 6x2x3 + 7x2 - 3x3
subject to
6x1 - 5x2 + x3 < -4
4x2 - x3 < 0
-2x1 + x2 + 2x3 < 5

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   1   25   -6
  25   -15   3
  -6   3   0

L =   0  
x1
  7
x2
  -3
x3



Outcome

fmin = f(X0) = -0,70326409495549

    X0   grad f   sum CkAk
x1
  -0,608308605341246   -0,51632047477745   -0,516320474777448
x2
  0,350148367952522   -25,5163204747775   -25,5163204747774
x3
  1,40059347181009   6,40059347181009   6,40059347181009
Ck - Lagrange multipliers at the Kuhn-Tucker,
Ak - vector coefficients of left side of constraints number "k",

Execution constraints and Lagrange multipliers
  AkX0     B     Ck
  -4
<
  -4
-
  -0,086053412462908
  0
<
  0
-
  -6,486646884273
  4,36795252225519
<
  5     0
Yellow highlighted lines that match the active inequalities at X.

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