Is there any method to linearize the following optimization problem?
\begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ &~~ x+|y| \leq 1 \\ &~~ (x,y)\in \{0,1\}*\{-1,0,1\} \end{align}
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Sign up to join this communityIs there any method to linearize the following optimization problem?
\begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ &~~ x+|y| \leq 1 \\ &~~ (x,y)\in \{0,1\}*\{-1,0,1\} \end{align}
I don’t have any to mind, but you can use a family of functions which are parameterized and smooth with absolute value as their limit. Then you can solve for multiple, usually shrinking, values of the parameter until you’re happy with the level of minimization.