Systems Optimization Laboratory
Stanford, CA 943054121 USA

User guide for MINOS 5.5: Fortran package for largescale 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 twophase primal simplex method is used.
The first phase minimizes the sum of infeasibilities.
For problems with linear constraints, a reducedgradient 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
doubleprecision 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.
B. A. Murtagh and M. A. Saunders (2003),
MINOS 5.51 User's Guide.
B. A. Murtagh and M. A. Saunders (1978).
Largescale
linearly constrained optimization,
Mathematical Programming 14, 4172.
B. A. Murtagh and M. A. Saunders (1982).
A projected
Lagrangian algorithm and its implementation
for sparse nonlinear constraints,
Mathematical Programming Study 16 (Constrained Optimization), 84117.