https://mintoc.de/index.php?title=Category:Implementation&feed=atom&action=history
Category:Implementation - Revision history
2024-03-28T09:51:41Z
Revision history for this page on the wiki
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https://mintoc.de/index.php?title=Category:Implementation&diff=1603&oldid=prev
FelixMueller at 12:58, 28 January 2016
2016-01-28T12:58:08Z
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FelixMueller
https://mintoc.de/index.php?title=Category:Implementation&diff=1599&oldid=prev
FelixMueller at 12:57, 28 January 2016
2016-01-28T12:57:30Z
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FelixMueller
https://mintoc.de/index.php?title=Category:Implementation&diff=1541&oldid=prev
SebastianSager: Moved explanation text from AMPL page
2016-01-28T08:52:54Z
<p>Moved explanation text from AMPL page</p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 08:52, 28 January 2016</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; 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>This category includes all subcategories <del class="diffchange diffchange-inline">regarding source code languages</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>This category includes all subcategories <ins class="diffchange diffchange-inline">that implement the MIOCP in a specific format of a solver</ins>. <ins class="diffchange diffchange-inline">These may of course be very different, depending on the particular approach to algorithmically solve the control problem.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bib id="Binder2001" />: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all-at-once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bib id="Bock1984" />,<bib id="Biegler1984" />, to (re)formulate the control problem by outer convexification <bib id="Sager2009" />, to use global optimization methods by under- and overestimators, e.g., <bib id="Esposito2000" />,<bib id="Papamichail2004" />,<bib id="Chachuat2006" />, to optimize the time-points for a given switching structure, e.g., <bib id="Kaya2003" />,<bib id="Gerdts2006" />,<bib id="Sager2009" />, to consider a static optimization problem instead of the transient behavior, e.g., <bib id="Grossmann2005" />, to approximate nonlinearities by piecewise-linear functions, e.g., <bib id="Martin2006" />, or by approximating the combinatorial decisions by continuous formulations, as in <bib id="Burgschweiger2009" /> for drinking water networks.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">We do not want to discuss these methods here, but rather refer to <bib id="Sager2009" />,<bib id="Sager2009b" /> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in some of the categories are only one out of many possible ways to formulate the underlying MIOCP problems.''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">== References ==</ins></div></td></tr>
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SebastianSager
https://mintoc.de/index.php?title=Category:Implementation&diff=1521&oldid=prev
FelixMueller: Created page with "This category includes all subcategories regarding source code languages. Category:Problem characterization Category:Main"
2016-01-27T18:17:13Z
<p>Created page with "This category includes all subcategories regarding source code languages. <a href="https://mintoc.de/index.php/Category:Problem_characterization" title="Category:Problem characterization">Category:Problem characterization</a> <a href="https://mintoc.de/index.php/Category:Main" title="Category:Main">Category:Main</a>"</p>
<p><b>New page</b></p><div>This category includes all subcategories regarding source code languages.<br />
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[[Category:Problem characterization]]<br />
[[Category:Main]]</div>
FelixMueller