Outer-approximation (OA)

Author: Yousef Aloufi (CHEME 6800 Fall 2021)

Example

Minimize $ {\displaystyle f(x)= y_{1} +y_{2} + \big(x_{1}\big)^{2} +\big(x_{2}\big)^{2} } $ Subject to $ {\displaystyle \big(x_{1}-2\big)^{2}-x_{2} \leq 0} $ $ {\displaystyle x_{1}-2y_{1} \geq 0} $ $ {\displaystyle x_{1}-x_{2}-3 \big(1-y_{1}\big) \geq 0} $ $ {\displaystyle x_{1}+y_{1}-1\geq 0} $ $ {\displaystyle x_{2}-y_{2}\geq 0} $ $ {\displaystyle x_{1}+x_{2}\geq 3y_{1}} $ $ {\displaystyle y_{1}+y_{2}\geq 1} $ $ {\displaystyle 0 \leq x_{1}\leq 4} $ $ {\displaystyle 0 \leq x_{2}\leq 4} $ $ {\displaystyle y_{1},y_{2} \in \big\{0,1\big\} } $