# 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> | ||

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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 16:39, 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 .