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\name{simplex.object}
\alias{simplex.object}
\title{
Linear Programming Solution Objects
}
\description{
Class of objects that result from solving a linear programming
problem using \code{simplex}.
}
\section{Generation}{
This class of objects is returned from calls to the function \code{simplex}.
}
\section{Methods}{
The class \code{"saddle.distn"} has a method for the function \code{print}.
}
\section{Structure}{
Objects of class \code{"simplex"} are implemented as a list with the
following components.
\describe{
\item{soln}{
The values of \code{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 \code{-1}
indicates that no feasible solution could be found. A value of
\code{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
\code{1} indicates that an optimal solution has been found.
}
\item{value}{
The value of the objective function at \code{soln}.
}
\item{val.aux}{
This is \code{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 \code{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 \code{m1+m2+m3} by \code{n+m1+m2}, where the final
\code{m1+m2} columns correspond to slack and surplus variables. If
no feasible solution is found there will be an additional
\code{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 \code{n+1} and \code{n+m1} correspond to slack
variables, those between \code{n+m1+1} and \code{n+m2} correspond to
surplus variables and those greater than \code{n+m2} are artificial
variables. Indices greater than \code{n+m2} should occur only if
\code{solved} is \code{-1} as the artificial variables are discarded in
the second stage of the simplex method.
}
\item{slack}{
The final values of the \code{m1} slack variables which arise when
the "<=" constraints are re-expressed as the equalities
\code{A1\%*\%x + slack = b1}.
}
\item{surplus}{
The final values of the \code{m2} surplus variables which arise when
the "<=" constraints are re-expressed as the equalities \code{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 \code{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.
}
}
}
\seealso{
\code{\link{print.simplex}}, \code{\link{simplex}}
}
\keyword{optimize}
\keyword{methods}
% Converted by Sd2Rd version 0.3-1.
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