User's guide for MINOS 5.5: a Fortran package for large-scale optimization

MINOS is a set of Fortran 77 subroutines for minimizing a general smooth function subject to linear constraints, nonlinear constraints, and simple upper and lower bounds. MINOS may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities. Ideally, the user should provide gradients of the nonlinear functions. (If necessary, MINOS will approximate the gradients by finite differences, but this could be slow and less reliable.)

If the objective function is convex and the constraints are linear, the solution obtained will be a global minimizer. Otherwise, the solution obtained will be a local minimizer.

For linear programs, a two-phase primal simplex method is used. The first phase minimizes the sum of infeasibilities. For problems with linear constraints, a reduced-gradient method is used. An approximate reduced Hessian is used to obtain search directions. The method is most efficient when many constraints or bounds are active at the solution.

For problems with nonlinear constraints, a linearly constrained Lagrangian method is used. This involves a sequence of major iterations, each of which solves (perhaps approximately) a linearly constrained subproblem. The subproblem objective is an augmented Lagrangian, and the subproblem constraints are linearizations of the nonlinear constraints at the current point.

MINOS is intended for large sparse problems. There is no fixed limit on problem size. Most working storage is contained in a single double-precision array (which should be sufficiently large). The source code is suitable for all scientific machines with a Fortran 77, 90, or 95 compiler.

B. A. Murtagh and M. A. Saunders (1998). MINOS 5.5 User's Guide (pdf)

B. A. Murtagh and M. A. Saunders (1978). Large-scale linearly constrained optimization, Math. Prog. 14, 41-72.

B. A. Murtagh and M. A. Saunders (1982). A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints, Math. Prog. Study 16 (Constrained Optimization), 84-117.