The Implementation of a Lagrangian-Based Algorithm for Sparse Nonlinear Constraints.

Abstract : An algorithm is described for solving large-scale nonlinear programs whose objective and constraint functions are smooth and continuously differentiable. The algorithm is of the augmented Lagrangian type, involving a sequence of sparse, linearly constrained subproblems whose objective functions include a modified Lagrangian term and a modified penalty function. The algorithm has been implemented in a general purpose Fortran code called MINOS/AUGMENTED. The system is intended for use on problems whose Jacobian matrix is sparse. (Such problems usually include a large set of purely linear constraints.) The bulk of the data may be assembled using a standard linear-programming matrix generator. Function and gradient values for all nonlinear terms are supplied by two user-written subroutines. Some aspects of the implementation are described in detail, and computational results are given for some nontrivial test problems. Assuming convergence occurs, the work involved is comparable to the solution of a moderate number of linear programs of similar size. (Author)

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