Original model
==============

Cost Function
-------------
 x

Constraints
-----------
 x ≤ x_max
 x ≥ x_min

With constraints relaxed equally
================================

Cost Function
-------------
 C

Constraints
-----------
 "minimum relaxation":
   C ≥ 1
 "relaxed constraints":
   x ≤ C·x_max
   x_min ≤ C·x

        ┃┓
   Cost╺┫┃
 (1.41) ┃┣╸x_min
        ┃┛ (2, fixed)



       ┃┓
       ┃┃
       ┃┣╸x ≤ C·x_max
       ┃┛
       ┃┓
       ┃┃
       ┃┣╸x_max = 1
 Model╺┫┛
       ┃┓
       ┃┃
       ┃┣╸x_min = 2
       ┃┛
       ┃┓
       ┃┃
       ┃┣╸x_min ≤ C·x
       ┃┛


Optimal Cost
------------
Relax.C : 1.414

WARNINGS
--------
Relaxed Constraints:
All constraints relaxed by 42%

Solution
--------
    x : 1.414
...constants
x_max : 1      (-0.5)
x_min : 2      (+0.5)

Relax
C : 1.414

Most Sensitive Constraints
--------------------------
+0.5 : x ≤ C·x_max
+0.5 : x_min ≤ C·x

C (1.41)
  breaks down into:
    C (1.41)
      which in: x ≤ C·x_max (sensitivity +0.5)
      { through a factor of 1/x_max (1, fixed) }
      breaks down into:
        x (1.41)
          which in: x_min ≤ C·x (sensitivity +0.5)
          breaks down into:
            { through a factor of 1/C (0.707) }
            x_min (2, fixed)

With constraints relaxed individually
=====================================

Cost Function
-------------
 C[:].prod()·x^0.01

Constraints
-----------
 "minimum relaxation":
   C[:] ≥ 1
 "relaxed constraints":
   x ≤ C[0]·x_max
   x_min ≤ C[1]·x

      ┃┓
 Cost╺┫┃
  (2) ┃┣╸1/x
      ┃┛ (1)



       ┃┓
       ┃┃
       ┃┣╸x_min = 2
       ┃┛
       ┃┓
       ┃┃
       ┃┣╸x_min ≤ C[1]·x
 Model╺┫┛
       ┃┓
       ┃┃
       ┃┣╸x ≤ C[0]·x_max
       ┃┛
       ┃┓
       ┃┃
       ┃┣╸x_max = 1
       ┃┛


Optimal Cost
------------
Relax1.C[:].prod()·x^0.01 : 2

WARNINGS
--------
Relaxed Constraints:
   1:  100% relaxed, from     x >= x_min
                       to x_min <= 2·x

Solution
--------
    x : 1
...constants
x_min : 2  (+1)
x_max : 1  (-0.99)

Relax1
C[:] : [ 1  2 ]

Most Sensitive Constraints
--------------------------
+1    : x_min ≤ C[1]·x
+0.99 : x ≤ C[0]·x_max
+0.01 : C[0] ≥ 1

With constants relaxed individually
===================================

Cost Function
-------------
 [Relax2.x_max, Relax2.x_min].prod()·x^0.01

Constraints
-----------
 Relax2
  "original constraints":
    x ≤ x_max
    x ≥ x_min
  "relaxation constraints":
    "x_max":
      Relax2.x_max ≥ 1
      x_max ≥ OriginalValues.x_max/Relax2.x_max
      x_max ≤ OriginalValues.x_max·Relax2.x_max
    "x_min":
      Relax2.x_min ≥ 1
      x_min ≥ OriginalValues.x_min/Relax2.x_min
      x_min ≤ OriginalValues.x_min·Relax2.x_min

      ┃┓
 Cost╺┫┃
  (2) ┃┣╸1/Relax2.x_min
      ┃┛ (0.5)



       ┃┓
       ┃┣╸x ≥ x_min
       ┃┛
       ┃┓
       ┃┃
       ┃┣╸x_min = 1
       ┃┛
       ┃┓
       ┃┃
 Model╺┫┣╸x_min ≥ OriginalValues.x_min/Relax2.x_min
       ┃┛
       ┃┓
       ┃┣╸x ≤ x_max
       ┃┛
       ┃┓
       ┃┣╸x_max = 1
       ┃┛
       ┃┓
       ┃┣╸x_max ≤ OriginalValues.x_max·Relax2.x_max
       ┃┛


Optimal Cost
------------
[Relax2.x_max, Relax2.x_min].prod()·x^0.01 : 2

WARNINGS
--------
Relaxed Constants:
  x_min: relaxed from 2 to 1

Solution
--------
    x : 1
x_max : 1
x_min : 1

Relax2
x_max : 1
x_min : 2

Relax2.OriginalValues
...constants
x_max : 1  (~0)
x_min : 2  (~0)

Most Sensitive Constraints
--------------------------
+1      : x ≥ x_min
+1      : x_min ≥ x_min/x_min
+0.9903 : x_max ≤ x_max·x_max
+0.99   : x ≤ x_max

