EVOLUTION-MANAGER
Edit File: simplex.object.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Linear Programming Solution Objects</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for simplex.object {boot}"><tr><td>simplex.object {boot}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2> Linear Programming Solution Objects </h2> <h3>Description</h3> <p>Class of objects that result from solving a linear programming problem using <code>simplex</code>. </p> <h3>Generation</h3> <p>This class of objects is returned from calls to the function <code>simplex</code>. </p> <h3>Methods</h3> <p>The class <code>"saddle.distn"</code> has a method for the function <code>print</code>. </p> <h3>Structure</h3> <p>Objects of class <code>"simplex"</code> are implemented as a list with the following components. </p> <dl> <dt>soln</dt><dd> <p>The values of <code>x</code> which optimize the objective function under the specified constraints provided those constraints are jointly feasible. </p> </dd> <dt>solved</dt><dd> <p>This indicates whether the problem was solved. A value of <code>-1</code> indicates that no feasible solution could be found. A value of <code>0</code> 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</code> indicates that an optimal solution has been found. </p> </dd> <dt>value</dt><dd> <p>The value of the objective function at <code>soln</code>. </p> </dd> <dt>val.aux</dt><dd> <p>This is <code>NULL</code> if a feasible solution is found. Otherwise it is a positive value giving the value of the auxiliary objective function when it was minimized. </p> </dd> <dt>obj</dt><dd> <p>The original coefficients of the objective function. </p> </dd> <dt>a</dt><dd> <p>The objective function coefficients re-expressed such that the basic variables have coefficient zero. </p> </dd> <dt>a.aux</dt><dd> <p>This is <code>NULL</code> 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. </p> </dd> <dt>A</dt><dd> <p>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</code> by <code>n+m1+m2</code>, where the final <code>m1+m2</code> columns correspond to slack and surplus variables. If no feasible solution is found there will be an additional <code>m1+m2+m3</code> columns for the artificial variables introduced to solve the first phase of the problem. </p> </dd> <dt>basic</dt><dd> <p>The indices of the basic (non-zero) variables in the solution. Indices between <code>n+1</code> and <code>n+m1</code> correspond to slack variables, those between <code>n+m1+1</code> and <code>n+m2</code> correspond to surplus variables and those greater than <code>n+m2</code> are artificial variables. Indices greater than <code>n+m2</code> should occur only if <code>solved</code> is <code>-1</code> as the artificial variables are discarded in the second stage of the simplex method. </p> </dd> <dt>slack</dt><dd> <p>The final values of the <code>m1</code> slack variables which arise when the "<=" constraints are re-expressed as the equalities <code>A1%*%x + slack = b1</code>. </p> </dd> <dt>surplus</dt><dd> <p>The final values of the <code>m2</code> surplus variables which arise when the "<=" constraints are re-expressed as the equalities <code>A2%*%x - surplus = b2</code>. </p> </dd> <dt>artificial</dt><dd> <p>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</code> 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. </p> </dd> </dl> <h3>See Also</h3> <p><code><a href="print.simplex.html">print.simplex</a></code>, <code><a href="simplex.html">simplex</a></code> </p> <hr /><div style="text-align: center;">[Package <em>boot</em> version 1.3-22 <a href="00Index.html">Index</a>]</div> </body></html>