http://tomwiki.com/index.php?title=SNOPT_File_Output&feed=atom&action=historySNOPT File Output - Revision history2024-03-29T11:20:15ZRevision history for this page on the wikiMediaWiki 1.39.1http://tomwiki.com/index.php?title=SNOPT_File_Output&diff=2843&oldid=prevBjorn: /* The major iteration log */2013-08-14T15:29:44Z<p><span dir="auto"><span class="autocomment">The major iteration log</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:29, 14 August 2013</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Minors ||is the number of iterations required by both the feasibility and optimality phases of the QP subproblem.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Minors ||is the number of iterations required by both the feasibility and optimality phases of the QP subproblem.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Generally, Minors will be 1 in the later iterations, since theoretical analysis predicts that the correct active set will be identified near the solution (see ''§''8.2).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Generally, Minors will be 1 in the later iterations, since theoretical analysis predicts that the correct active set will be identified near the solution (see <ins style="font-weight: bold; text-decoration: none;">[[SNOPT_Description_of_the_SQP_method|</ins>''§''8.2<ins style="font-weight: bold; text-decoration: none;">]]</ins>).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-valign="top"</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Step||The step length ''a ''taken along the current search direction ''p''. The variables ''x ''have just been changed to ''x ''+ ''ap''. On reasonably well-behaved problems, the unit step will be taken as the solution is approached.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Step||The step length ''a ''taken along the current search direction ''p''. The variables ''x ''have just been changed to ''x ''+ ''ap''. On reasonably well-behaved problems, the unit step will be taken as the solution is approached.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Optimal||is the value of maxgap, the maximum complementarity gap (56). It is an estimate of the degree of nonoptimality of the reduced costs. Both Feasbl and Optimal are small in the neighborhood of a solution.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|Optimal||is the value of maxgap, the maximum complementarity gap (56). It is an estimate of the degree of nonoptimality of the reduced costs. Both Feasbl and Optimal are small in the neighborhood of a solution.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-valign="top"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-valign="top"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|MeritFunction||is the value of the augmented Lagrangian merit function (see (53)). This function will decrease at each iteration unless it was necessary to increase the penalty parameters (see ''§''8.2). As the solution is approached, Merit will converge to the value of the objective at the solution.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|MeritFunction||is the value of the augmented Lagrangian merit function (see (53)). This function will decrease at each iteration unless it was necessary to increase the penalty parameters (see <ins style="font-weight: bold; text-decoration: none;">[[SNOPT_Description_of_the_SQP_method|</ins>''§''8.2<ins style="font-weight: bold; text-decoration: none;">]]</ins>). As the solution is approached, Merit will converge to the value of the objective at the solution.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In elastic mode, the merit function is a composite function involving the constraint violations weighted by the elastic weight.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In elastic mode, the merit function is a composite function involving the constraint violations weighted by the elastic weight.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|nS||The current number of superbasic variables.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|nS||The current number of superbasic variables.</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|CondHz||An estimate of the condition number of ''RTR'', an estimate of ''Z TH Z '', the reduced Hessian of the La- grangian. It is the square of the ratio of the largest and smallest diagonals of the upper triangular matrix ''R ''(which is a lower bound on the condition number of ''RT R''). Cond Hz gives a rough indica- tion of whether or not the optimization procedure is having difficulty. If ''E ''is the relative precision of the machine being used, the SQP algorithm will make slow progress if Cond Hz becomes as large as &epsilon;<<del style="font-weight: bold; text-decoration: none;">syo</del>>-1/2</sup> &asymp; 10<sup>8</sup> , and will probably fail to find a better solution if Cond Hz reaches &epsilon;<sup>-3/4</sup> &asymp; 10<sup>12</sup> .</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|CondHz||An estimate of the condition number of ''RTR'', an estimate of ''Z TH Z '', the reduced Hessian of the La- grangian. It is the square of the ratio of the largest and smallest diagonals of the upper triangular matrix ''R ''(which is a lower bound on the condition number of ''RT R''). Cond Hz gives a rough indica- tion of whether or not the optimization procedure is having difficulty. If ''E ''is the relative precision of the machine being used, the SQP algorithm will make slow progress if Cond Hz becomes as large as &epsilon;<<ins style="font-weight: bold; text-decoration: none;">sup</ins>>-1/2</sup> &asymp; 10<sup>8</sup> , and will probably fail to find a better solution if Cond Hz reaches &epsilon;<sup>-3/4</sup> &asymp; 10<sup>12</sup> .</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To guard against high values of Cond Hz, attention should be given to the scaling of the variables and the constraints. In some cases it may be necessary to add upper or lower bounds to certain variables to keep them a reasonable distance from singularities in the nonlinear functions or their derivatives.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To guard against high values of Cond Hz, attention should be given to the scaling of the variables and the constraints. In some cases it may be necessary to add upper or lower bounds to certain variables to keep them a reasonable distance from singularities in the nonlinear functions or their derivatives.</div></td></tr>
</table>Bjornhttp://tomwiki.com/index.php?title=SNOPT_File_Output&diff=2574&oldid=prevElias at 17:41, 18 January 20122012-01-18T17:41:20Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:41, 18 January 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This exit implies that there may be errors in the subroutines that define the problem objective and constraints. If the objective derivatives appear to incorrect, a check has been made on some individual elements of the objective gradient array at the first point that satisfies the linear constraints. At least one component (G(''k'') or gObj(''j'') ) is being set to a value that disagrees markedly with its associated forward-difference estimate <math>\partial f_0 / \partial x_j</math>. (The relative difference between the computed and estimated values is 1.0 or more.) This exit is a safeguard, since SNOPT will usually fail to make progress when the computed gradients are seriously inaccurate. In the process it may expend considerable effort before terminating with INFO 41 above.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This exit implies that there may be errors in the subroutines that define the problem objective and constraints. If the objective derivatives appear to incorrect, a check has been made on some individual elements of the objective gradient array at the first point that satisfies the linear constraints. At least one component (G(''k'') or gObj(''j'') ) is being set to a value that disagrees markedly with its associated forward-difference estimate <math>\partial f_0 / \partial x_j</math>. (The relative difference between the computed and estimated values is 1.0 or more.) This exit is a safeguard, since SNOPT will usually fail to make progress when the computed gradients are seriously inaccurate. In the process it may expend considerable effort before terminating with INFO 41 above.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Check the function and gradient computation ''very carefully''. A simple omission (such as forgetting to divide ''f''<sub>0</sub> by 2) could explain everything. If ''f''<sub>0</sub> or a component <math>partial <del style="font-weight: bold; text-decoration: none;">\Obj</del>/\partial x_j</math> is very large, then give serious thought to scaling the function or the nonlinear variables.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Check the function and gradient computation ''very carefully''. A simple omission (such as forgetting to divide ''f''<sub>0</sub> by 2) could explain everything. If ''f''<sub>0</sub> or a component <math><ins style="font-weight: bold; text-decoration: none;">\</ins>partial <ins style="font-weight: bold; text-decoration: none;">f_0 </ins>/ \partial x_j</math> is very large, then give serious thought to scaling the function or the nonlinear variables.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If you feel ''certain ''that the computed gObj(''j'') is correct (and that the forward-difference estimate is therefore wrong), you can specify Verify level 0 to prevent individual elements from being checked. However, the opti- mization procedure may have difficulty.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If you feel ''certain ''that the computed gObj(''j'') is correct (and that the forward-difference estimate is therefore wrong), you can specify Verify level 0 to prevent individual elements from being checked. However, the opti- mization procedure may have difficulty.</div></td></tr>
</table>Eliashttp://tomwiki.com/index.php?title=SNOPT_File_Output&diff=1162&oldid=prevElias: Created page with "{{Part Of Manual|title=the SNOPT Manual|link=SNOPT}} The files can be directed with the Print file and Summary file options (or suppressed). ==The PRINT file== If Pri..."2011-10-13T13:24:50Z<p>Created page with "{{Part Of Manual|title=the SNOPT Manual|link=<a href="/index.php?title=SNOPT" title="SNOPT">SNOPT</a>}} The files can be directed with the Print file and Summary file options (or suppressed). ==The PRINT file== If Pri..."</p>
<a href="http://tomwiki.com/index.php?title=SNOPT_File_Output&diff=1162">Show changes</a>Elias