Expression 8: negative "x" minus "y" less than or equal to 0−x−y≤0
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Expression 9: "y" minus 2 "x" minus 1 less than or equal to 0y−2x−1≤0
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Expression 10: "y" plus 2 "x" minus 1 less than or equal to 0y+2x−1≤0
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The region that you want is the only place where ALL of the expressions on the left-hand sides of these inequalities are less than zero. This can be expressed as:
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Expression 12: max left parenthesis, "x" minus "y" , negative "x" minus "y" , "y" minus 2 "x" minus 1 , "y" plus 2 "x" minus 1 , right parenthesis less than or equal to 0maxx−y,−x−y,y−2x−1,y+2x−1≤0
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When the region is not convex, you could either divide it up into regions that are convex or deal with the indented edges in this way:
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Expression 14: max left parenthesis, "x" minus 2 minus "y" , 2 minus "x" minus "y" , min left parenthesis, "y" minus 1.5 plus 0.5 "x" , "y" plus 0.5 minus 0.5 "x" , right parenthesis , right parenthesis less than or equal to 0maxx−2−y,2−x−y,miny−1.5+0.5x,y+0.5−0.5x≤0