GAMS — The Solver Manuals - Available Software

348 MINOS
MINOS-Link May 25, 2002 WIN.M5.M5 20.6 023.046.040.VIS GAMS/MINOS 5.5
GAMS/MINOS, Large Scale Nonlinear Solver
B. A. Murtagh, University of New South Wales
P. E. Gill, University of California at San Diego,
W. Murray, M. A. Saunders, and M. H. Wright,
Systems Optimization Laboratory, Stanford University
Work space allocated -- 2.01 Mb
Reading Rows...
Reading Columns...
Reading Instructions...
Major minor step objective Feasible Optimal nsb ncon penalty BSswp
1 2T 0.0E+00 0.00000E+00 1.8E+02 2.0E-01 0 1 1.0E+00 0
2 90 1.0E+00 1.91735E+02 1.5E-03 7.6E+00 0 3 1.0E+00 0
3 0 1.0E+00 1.91735E+02 1.3E-09 5.5E-06 0 4 1.0E+00 0
4 0 1.0E+00 1.91735E+02 1.4E-12 2.9E-13 0 5 1.0E-01 0
EXIT - Optimal Solution found, objective: 191.7346
--- Restarting execution
--- CAMCGE.GMS(450) 0 Mb
--- Reading solution for model camcge
*** Status: Normal completion
Two sets of iterations - Major and Minor, are now reported. A description of the various columns present in this
log file follows:
Major A major iteration involves linearizing the nonlinear constraints and performing a number of minor iterations
on the resulting subproblem. The objective for the subproblem is an augmented Lagrangian, not the
true objective function.
minor The number of minor iterations performed on the linearized subproblem. If it is a simple number like
90, then the subproblem was solved to optimality. Here, 2T means that the subproblem was terminated.
In general the T is not something to worry about. Other possible flags are I and U, which mean that the
subproblem was Infeasible or Unbounded. MINOS may have difficulty if these keep occurring.
step The step size taken towards the solution suggested by the last major iteration. Ideally this should be 1.0,
especially near an optimum. If the subproblem solutions are widely different, MINOS may reduce the step
size under control of the Major Damping parameter.
objective The objective function for the original nonlinear program.
Feasible Primal infeasibility, indicating the maximum non-linear constraint violation.
Optimal The maximum dual infeasibility, measured as the maximum departure from complementarity. If we
call d j the reduced cost of variable x j , then the dual infeasibility of x j is d j × min{x j − l j , 1} or −d j ×
min{u j − x j , 1} depending on the sign of d j .
nsb Number of superbasics. If the model is feasible this number cannot exceed the superbasic limit, which may
need to be reset to a larger number if the numbers in this column become larger.
ncon The number of times MINOS has evaluated the nonlinear constraints and their derivatives.
penalty The current value of the penalty parameter in the augmented Lagrangian (the objective for the subproblems).
If the major iterations appear to be converging, MINOS will decrease the penalty parameter. If
there appears to be difficulty, such as unbounded subproblems, the penalty parameter will be increased.