Difference between revisions of "Optimization with absolute values"

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==Numerical Example==
 
==Numerical Example==
  
<math>\ Min      |x_1| + 2|x_2| + |x_3| </math><br>  
+
<math>\ min |x_1| + 2|x_2| + |x_3| </math><br>  
 
<math>\ s.t.      x_1 + x_2 - x_3 \le 10</math>
 
<math>\ s.t.      x_1 + x_2 - x_3 \le 10</math>
  
Line 29: Line 29:
 
The problem has now been reformulated as a linear programming problem that can be solved normally:
 
The problem has now been reformulated as a linear programming problem that can be solved normally:
  
<math>\ Min  U_1 + 2U_2 + U_3 </math><br>  
+
<math>\min U_1 + 2U_2 + U_3 </math><br>  
  
 
<math>\            s.t.    x_1 + x_2 - x_3 \le 10</math>
 
<math>\            s.t.    x_1 + x_2 - x_3 \le 10</math>

Revision as of 16:36, 20 November 2020

Authors: Matthew Chan (mdc297), Yilian Yin (), Brian Amado (ba392), Peter (pmw99), Dewei Xiao (dx58) - SYSEN 5800 Fall 2020

Steward: Fengqi You


Numerical Example


We replace the absolute value quantities with a single variable:

We must introduce additional constraints to ensure we do not lose any information by doing this substitution:

The problem has now been reformulated as a linear programming problem that can be solved normally:


The optimum value for the objective function is , which occurs when and and .