/
relaxation_output.txt
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/
relaxation_output.txt
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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
┃┛
~~~~~~~~
WARNINGS
~~~~~~~~
Relaxed Constraints
-------------------
All constraints relaxed by 42%
~~~~~~~~
Free Variables
--------------
x : 1.414
| Relax
C : 1.414
Fixed Variables
---------------
x_max : 1
x_min : 2
Variable Sensitivities
----------------------
x_max : -0.5
x_min : +0.5
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
┃┛
~~~~~~~~
WARNINGS
~~~~~~~~
Relaxed Constraints
-------------------
1: 100% relaxed, from x >= x_min
to x_min <= 2·x
~~~~~~~~
Free Variables
--------------
x : 1
| Relax1
C : [ 1 2 ]
Fixed Variables
---------------
x_max : 1
x_min : 2
Variable Sensitivities
----------------------
x_min : +1
x_max : -0.99
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
┃┛
~~~~~~~~
WARNINGS
~~~~~~~~
Relaxed Constants
-----------------
x_min: relaxed from 2 to 1
~~~~~~~~
Free Variables
--------------
x : 1
x_max : 1
x_min : 1
| Relax2
x_max : 1
x_min : 2
Fixed Variables
---------------
| Relax2.OriginalValues
x_max : 1
x_min : 2
Variable Sensitivities
----------------------
x_min : +1
x_max : -0.99
Most Sensitive Constraints
--------------------------
+1 : x ≥ x_min
+1 : x_min ≥ OriginalValues.x_min/Relax2.x_min
+0.99 : x ≤ x_max
+0.99 : x_max ≤ OriginalValues.x_max·Relax2.x_max