Projection methods for non-linear programming

Several algorithms are presented for solving the non-linear programming problem, based on “variable-metric” projections of the gradient of the objective function into a local approximation to the constraints. The algorithms differ in the nature of this approximation. Inequality constraints are dealt with by selecting at each step a subset of “active” constraints to treat as equalities, this subset being the smallest necessary to ensure that the new point remains feasible. Some numerical results are given for the Colville problems.