simplex
.simplex
."saddle.distn"
has a method for the function print
."simplex"
are implemented as a list with the following
components.
item{soln}{
The values of x
which optimize the objective function under the specified
constraints provided those constraints are jointly feasible.
}
item{solved}{
This indicates whether the problem was solved. A value of -1
indicates that
no feasible solution could be found. A value of 0
that the maximum number
of iterations was reached without termination of the second stage. This may
indicate an unbounded function or simply that more iterations are needed.
A value of 1
indicates that an optimal solution has been found.
}
item{value}{
The value of the objective function at soln
.
}
item{val.aux}{
This is NULL
if a feasible solution is found. Otherwise it is a positive
value giving the value of the auxiliary objective function when it was
minimized.
}
item{obj}{
The original coefficients of the objective function.
}
item{a}{
The objective function coefficients re-expressed such that the basic variables
have coefficient zero.
}
item{a.aux}{
This is NULL
if a feasible solution is found. Otherwise it is the
re-expressed auxiliary objective function at the termination of the first
phase of the simplex method.
}
item{A}{
The final constraint matrix which is expressed in terms of the non-basic
variables. If a feasible solution is found then this will have dimensions
m1+m2+m3
by n+m1+m2
, where the final m1+m2
columns correspond to slack
and surplus variables. If no feasible solution is found there will be an
additional m1+m2+m3
columns for the artificial variables introduced to solve
the first phase of the problem.
}
item{basic}{
The indices of the basic (non-zero) variables in the solution. Indices
between n+1
and n+m1
correspond to slack variables, those between n+m1+1
and n+m2
correspond to surplus variables and those greater than n+m2
are
artificial variables. Indices greater than n+m2
should occur only if solved
is -1
as the artificial variables are discarded in the second stage of the
simplex method.
}
item{slack}{
The final values of the m1
slack variables which arise when the "<="
constraints are re-expressed as the equalities A1%*%x + slack = b1
.
}
item{surplus}{
The final values of the m2
surplus variables which arise when the "<="
constraints are re-expressed as the equalities A2%*%x - surplus = b2
.
}
item{artificial}{
This is NULL if a feasible solution can be found. If no solution can be found
then this contains the values of the m1+m2+m3
artificial variables which
minimize their sum subject to the original constraints. A feasible solution
exists only if all of the artificial variables can be made 0 simultaneously.
}
print.simplex
, simplex