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Post Closed as "Not suitable for this site" by Will Jagy, Chris Godsil, Steven Landsburg, Andrey Rekalo, Stefan Kohl♦
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Gecko
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I have a series of similar linear programs that depend on an input vector $a\in A$ and whose solution is an output vector $b\in B$. I can solve them individually, but this is wasteful. I suspect that for a small $A$ there are linear mapping from elements in $A$ to elements in $B$. I want to discover this mapping to avoid solving the linear program every time.

What can I do to discover this formula? My current approach is to solve various of these problems and use them solutions to solve a system of linear equations. It works, but it is not very elegant. Are there any standard approaches to accomplish this?

Edit: Just to be clear, I think robust linear programming does not cut it, there the problem is still to find a single feasible solution for a range of parameters, not an solution that depends on the input.

I have a series of similar linear programs that depend on an input vector $a\in A$ and whose solution is an output vector $b\in B$. I can solve them individually, but this is wasteful. I suspect that for a small $A$ there are linear mapping from elements in $A$ to elements in $B$. I want to discover this mapping to avoid solving the linear program every time.

What can I do to discover this formula? My current approach is to solve various of these problems and use them solutions to solve a system of linear equations. It works, but it is not very elegant. Are there any standard approaches to accomplish this?

I have a series of similar linear programs that depend on an input vector $a\in A$ and whose solution is an output vector $b\in B$. I can solve them individually, but this is wasteful. I suspect that for a small $A$ there are linear mapping from elements in $A$ to elements in $B$. I want to discover this mapping to avoid solving the linear program every time.

What can I do to discover this formula? My current approach is to solve various of these problems and use them solutions to solve a system of linear equations. It works, but it is not very elegant. Are there any standard approaches to accomplish this?

Edit: Just to be clear, I think robust linear programming does not cut it, there the problem is still to find a single feasible solution for a range of parameters, not an solution that depends on the input.

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Gecko
Gecko
  • 109
  • 3

generalization from linear programming solution

I have a series of similar linear programs that depend on an input vector $a\in A$ and whose solution is an output vector $b\in B$. I can solve them individually, but this is wasteful. I suspect that for a small $A$ there are linear mapping from elements in $A$ to elements in $B$. I want to discover this mapping to avoid solving the linear program every time.

What can I do to discover this formula? My current approach is to solve various of these problems and use them solutions to solve a system of linear equations. It works, but it is not very elegant. Are there any standard approaches to accomplish this?