An economical method of calculating Lagrange multiplier estimates for nonlinear programming problems when many of the constraints are bounds on the variables

Some recent methods for solving nonlinear programming problems make use of estimates of the Lagrange multipliers. These estimates are usually calculated by solving a system oft linear equations, wheret is the number of active constraints. It is shown that, when a large proportion of the active constraints consists of simple upper or lower bounds on the variables, then computational effort can be saved by means of a reorganization of this linear system.