Outer-approximation (OA)

Author: Yousef Aloufi (CHEME 6800 Fall 2021)

Example

Minimize

$$f(x)=y_{1}+y_{2}+{\big (}x_{1}{\big )}^{2}+{\big (}x_{2}{\big )}^{2}$$

Subject to

$${\big (}x_{1}-2{\big )}^{2}-x_{2}\leq 0$$

$$x_{1}-2y_{1}\geq 0$$

$$x_{1}-x_{2}-3{\big (}1-y_{1}{\big )}\geq 0$$

$$x_{1}+y_{1}-1\geq 0$$

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{2}-y_{2}\geq 0} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{1}+x_{2}\geq 3y_{1}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{1}+y_{2}\geq 1} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 \leq x_{1},x_{2} \leq 4} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_{1},y_{2} \in \big\{0,1\big\} }