A simplex dictionary expresses the basic variables and the objective as affine functions of the nonbasic variables in a linear program. Setting the nonbasic variables to zero gives a basic feasible solution when all basic values are nonnegative. A simplex algorithm pivot exchanges one basic and one nonbasic variable. For maximization, a feasible dictionary with all nonbasic objective coefficients nonpositive certifies optimality.
New to topics? Read the docs here!