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's gravatar image

Giovanni
112
accept rate: 0%


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].

link

answered 27 Oct '14, 14:33

fbahr's gravatar image

fbahr ♦
4.6k716
accept rate: 13%

edited 27 Oct '14, 14:36

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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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