Solving Large Sparse Nonlinear Programs Using GRG

Abstract

We describe a feasibility-retaining GRG algorithm for large sparse nonlinear programs of general form. Its FORTRAN implementation, LSGRG, is enhanced by heuristics which aid in basis selection, combatting degeneracy, dynamic tolerance adjustment, and predicting Newton failures. Key roles are also played by efficient procedures for basis inversion and by both pure and limited memory BFGS methods for computing the search direction. The design goal for LSGRG is maximum reliability with at least acceptable speed. Extensive computational tests on both FORTRAN and GAMS models indicate that LSGRG is promising in this regard. Comparisons are presented with GRG2, a sparsity oriented SQP code, and MINOS, indicating that LSGRG is a useful complement to MINOS in a multi-solver NLP environment. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.