Outer-approximation (OA): Difference between revisions
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== Example == | == Example == | ||
Minimize <math display=block> f(x)= y_{1} +y_{2} + \big(x_{1}\big)^{2} +\big(x_{2}\big)^{2} </math> | |||
Subject to <math display=block>\big(x_{1}-2\big)^{2}-x_{2} \leq 0</math> | |||
<math display=block>x_{1}-2y_{1} \geq 0</math> | |||
<math display=block>x_{1}-x_{2}-3 \big(1-y_{1}\big) \geq 0</math> | |||
<math display=block>x_{1}+y_{1}-1\geq 0</math> | |||
<math display=block>x_{2}-y_{2}\geq 0</math> | |||
<math display=block>x_{1}+x_{2}\geq 3y_{1}</math> | |||
<math display=block>y_{1}+y_{2}\geq 1</math> | |||
<math display=block>0 \leq x_{1} \leq 4</math> | |||
<math display=block>0 \leq x_{2} \leq 4</math> | |||
<math display=block>y_{1},y_{2} \in \big\{0,1\big\} </math> | |||
==Conclusion== | ==Conclusion== | ||
==References== | ==References== |
Revision as of 05:19, 26 November 2021
Author: Yousef Aloufi (CHEME 6800 Fall 2021)
Introduction
Theory
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 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 \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} 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}-3 \big(1-y_{1}\big) \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}+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} \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 0 \leq 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\} }