Optimization with absolute values

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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:

Failed to parse (unknown function "\s"): {\displaystyle \begin{align} \s.t. x_1 + x_2 - x_3 \le 10 \\ x_1 - 3x_2 + 2x_3= 12 \end{align}}

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