Simplex Method
An algorithm for solving linear programming problems by moving along the edges of the feasible region to find the optimal vertex.
Explanation
The simplex method, developed by George Dantzig in 1947, is one of the most important algorithms in optimization. It works by starting at a feasible vertex of the constraint polytope and moving to adjacent vertices that improve the objective function until no further improvement is possible. Despite exponential worst-case complexity, it performs efficiently in practice.
How kint Uses It
kint uses the simplex method (and dual simplex) as the workhorse for solving LP relaxations within branch-and-bound for MIP problems. Modern implementations in Gurobi and CPLEX solve LPs with millions of variables in seconds.
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