Outer-approximation (OA)

Author: Yousef Aloufi (CHEME 6800 Fall 2021)

Example

Minimize 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 f(x)= y_{1} +y_{2} + \big(x_{1}\big)^{2} +\big(x_{2}\big)^{2} } Subject to

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

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}-2y_{1} \geq 0}

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

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

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

$$x_{1}+x_{2}\geq 3y_{1}$$

$$y_{1}+y_{2}\geq 1$$

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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\} }