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Problem Restated The problem is to find the minimum of the cost defined by, $$\sum_{k=0}^3 x_k^2 + u_k^2$$ with the initial condition $x_0=5$ and relation $0\le x_{k+1}=x_k+u_k\le5$. Simple Arithmetic  x_0=5\ \stackrel{u_0=-3}{\xrightarrow{\hspace{2em}}}\ x_1=2\ \stackrel{u_1=-1}{\xrightarrow{\hspace{2em}}}\ x_2=1\ \stackrel{u_2=-1}{\xrightarrow{\...

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In the minimum edge cover problem, you have to find a smallest set of edges that covers all of the vertices. The first thing you want to do is decide which edges you want to include in your edge cover. This can be done by having a variable $x_e\in \{0, 1\}$ for each edge $e$ of the graph. If $x_e=1$, you include the edge $e$ in your graph. If $x_e=0$, you ...

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In constraint programming this particular type of constraint is known as a table constraint. It is generally said to be an existential constraint, since many other constraints can be encoded using a table constraint. As such, it is often better to use the underlying structure when possible (I don't see a way around it in this case), although tables have been ...

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