A method is presented for computing the optimum value of a quadratic functional subject to linear inequalities, which rapidly ascertains which, if any, of the inequalities are binding at the optimum point. The method resembles that of H. Theil and C. Van de Panne, but no combinatorial analysis needs be performed to isolate the binding constraints. All violated constraints are imposed as equalities, and those with positive Lagrangian multipliers are retained. Contradictory equalities are automatically resolved by the use of the generalized inverse. The method appears most useful in systems with large numbers of variables and constraints.