# Convert NLP constraint into a linear one

 0 Hy, I have a problem with a non linear constraint. In an Optimization problem i have this constraint X*Y >= K with X,Y continuous variables and bounded (X€[Xm,XM] Y€[Ym,YM]) and K constant.  There is some way to convert this non linear constraint into a linear one (i mean a set of linear). Thanks asked 27 Oct '14, 11:49 Giovanni 11●1 accept rate: 0%

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 2 With $$Z_1 = \frac{1}{2}(X + Y)$$ and $$Z_2 = \frac{1}{2}(X - Y)$$ $$\Rightarrow$$ $$X * Y = Z_1^2 - Z_2^2$$, and – hence – $$X * Y \ge K \Leftrightarrow Z_1^2 - Z_2^2 \ge K$$ ...which allows for piecewise linear approximation [using λ-formulation, SOS2 variables, and/or other fancy stuff your modeling language + solver support]. answered 27 Oct '14, 14:33 fbahr ♦ 4.6k●7●16 accept rate: 13%
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Asked: 27 Oct '14, 11:49

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Last updated: 27 Oct '14, 14:36

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