#18735: MixedIntegerLinearProgram/HybridBackend: Reconstruct exact
rational/algebraic basic solution
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Reporter: mkoeppe | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: numerical | Resolution:
Keywords: lp | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #18685, #18688, #20296 | Stopgaps:
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Changes (by mkoeppe):
* dependencies: #18685, #18688 => #18685, #18688, #20296
Old description:
> Sometimes one can use a fast numerical LP solver to solve a problem to
> "optimality",
> then reconstruct the primal and dual solution in rational arithmetic (or
> over whatever base_ring was used...) and in this way prove that this
> basis is indeed optimal.
> `MixedIntegerLinearProgram` should support this mode of operation.
>
> This would be particularly interesting in conjunction with #18764. (But
> see #18765 for a different approach.)
>
> #18685 provides the necessary basis-status functions (for the GLPK
> backend).
> #18688 provides a solver-independent interface to these functions.
>
> The reconstructed solution could be presented via #20296.
New description:
Sometimes one can use a fast numerical LP solver to solve a problem to
"optimality",
then reconstruct the primal and dual solution in rational arithmetic (or
over whatever base_ring was used...) and in this way prove that this basis
is indeed optimal.
`MixedIntegerLinearProgram` should support this mode of operation.
The current branch, on top of #20926, attempts to do this by implementing
a `HybridBackend`, which delegates to two backends:
- a fast, possibly inexact backend (Gurobi or GLPK or even GLPK with
glp_exact -- see #18764)
- a slow, exact one that can set the simplex basis (only
`InteractiveLPBackend` fits the bill - from #20296)
#18685 provides the necessary basis-status functions (for the GLPK
backend).
#18688 provides a solver-independent interface to these functions.
#18804 exposes basis status via backend dictionaries.
--
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Ticket URL: <http://trac.sagemath.org/ticket/18735#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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