# Simplex optimality tolerance

## Question

What does the simplex optimality tolerance parameter signify?

While solving a model using Simplex, the algorithm stops when a basic feasible solution with non-negative reduced costs is found. The solution thus found is optimal for the underlying LP since the objective can no longer be improved in the absence of a basis variable with a negative reduced cost. CPLEX determines the non-negativity of a reduced cost using the simplex optimality tolerance (EpOpt / CPX_PARAM_EPOPT) parameter. Specifically, a negative reduced cost whose absolute value is less than the optimality tolerance would still be considered non-negative.

As an example, if the optimality tolerance set at 1e-6, then a variable with a reduced cost of -1e9 would be deemed non-negative.

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Modified date:
16 June 2018

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