# convert non linear function to linear

 0 1 Hi Dear Are there anybody that know how to convert this function to linear? min⁡〖∑(k=1)^K▒∑(i=3)^I▒∑(t=1)^T▒〖(( i * N_it^k )-(i^' * 〖N'〗( i^' t)^k))〗^2 〗 N_it^k and 〖N'〗_( i^' t)^k) are binary variable asked 13 Nov '16, 02:01 coolman 15●2 accept rate: 0% Rob Pratt 1.2k●2●6

 0 Your formula is a bit mangled, but if I understand correctly, you can linearize as follows. Expand the summand to get an expression of the form $$a x^2 + b y^2 + c x y$$, where $$x$$ and $$y$$ are binary variables. Then replace $$x^2$$ and $$y^2$$ with $$x$$ and $$y$$, respectively. Finally, perform the usual linearization of the product of binary variables to replace $$x y$$ with binary variable $$z$$, yielding $$a x + b y + c z$$. answered 13 Nov '16, 08:27 Rob Pratt 1.2k●2●6 accept rate: 28% thank you about your answer and excuse me for not clearing of formula, most recently i find this site and i have problem with writing formula. (13 Nov '16, 23:45) coolman
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