Linear programming is usually a Specific situation of mathematical programming (also referred to as mathematical optimization).
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This intently associated list of problems has been cited by Stephen Smale as Among the many 18 best unsolved difficulties from the twenty first century. In Smale's terms, the 3rd Model of the problem "is the key unsolved trouble of linear programming principle." When algorithms exist to unravel linear programming in weakly polynomial time, like the ellipsoid strategies and interior-place techniques, no algorithms have but been observed that allow for strongly polynomial-time performance in the volume of constraints and the quantity of variables.
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It has been proved that all polytopes have subexponential diameter. The the latest disproof of your Hirsch conjecture is the initial step to confirm no matter if any polytope has superpolynomial diameter. If any this kind of polytopes exist, then no edge-next variant can operate in polynomial time. Questions about polytope diameter are of unbiased mathematical desire.
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