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Mathematics
General Math
Does 'rest' have a precise mathematical definition?
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[QUOTE="jbriggs444, post: 6899624, member: 422467"] It occurs to me that the notion of "resting on" would make the most sense in an environment where a line segment or point is free to move within some bounded region. This could occur for a linear optimization problem and is a key way of thinking about the [URL='https://en.wikipedia.org/wiki/Simplex_algorithm']Simplex method[/URL]. The idea is that one is trying to optimize a formula which is a linear combination of some finite set of parameters while adhering to a set of constraints. Each constraint is a linear inequality involving some or all of those parameters. The geometric insight is that the constraints amount to oriented hyperplanes cutting through an n-dimensional space. They are the boundaries to a (hopefully non-empty) region. Importantly, the region will be convex. So a hill climbing approach is sure to succeed. One starts by finding an n-tuple that is a feasible solution (it is the coordinates for a point within the non-empty region). One then walks the solution to a boundary of the region. Once the solution is "[B]resting on[/B]" a boundary, one can walk it along the edges until an optimal corner, edge or face is found. The process bears a striking resemblance to Gaussian elimination. For instance, one can try to optimize a mix of grains for pig feed where each feed has a unit cost and one is trying to satisfy inequalities involving various amino acid requirements that must be met while minimizing feed cost. e.g. [URL]https://www.jstor.org/stable/25556356[/URL]. [It's been over 40 years since I wrote code for such a thing -- I went to school in Iowa, a state where there are about seven times more pigs than people] [/QUOTE]
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Does 'rest' have a precise mathematical definition?
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