First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems
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Ohio University / OhioLINK
2004
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1091111473 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-ohiou10911114732021-08-03T05:43:07Z First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems Voisei, Mircea D. Optimization Optimal Control Generalized Gradient Elliptic Equations <p>The aim of this dissertation is to provide first-order necessary conditions of optimality for local optimal solutions <i>x</i><sup>*</sup> of the problem</p> <p>Minimize <i>L</i>(<i>x</i>), subject to ƒ(<i>x</i>) ∈ <i>Ax</i>,</p> <p>where (<i>X</i>,‖ · ‖ <sub>X</sub>),(<i>Y</i>,‖ · ‖ <sub><i>Y</i></sub>) are Banach spaces, <i>L</i> : <i>X</i> → <i>I̅R̅</i>, ƒ : <i>X</i> → <i>Y</i>, and <i>A</i> : <i>X</i> → 2<sup>Y</sup>. Here <i>L</i> is locally Lipschitz continuous or of the form <i>g</i>(<i>y</i>) + <i>h</i>(<i>u</i>), where <i>x</i> = (<i>y,u</i>), <i>g</i> is locally Lipschitz continuous, and <i>h</i> is proper convex lower semicontinuous, ƒ is locally Lipschitz continuous or constant, and <i>A</i> is linear or strongly monotone.</p> <p>The main part of this dissertation deals with the construction of a general approach to the maximum principle followed by direct applications of the maximum principle to optimal control problems governed by abstract state equations.</p> <p>This dissertation concludes by presenting two specific examples of applications of our necessary optimality conditions to problems governed by nonlinear partial differential equations of elliptic type. The necessary conditions are given in terms of Clarke's generalized gradient and Jacobian.</p> 2004-07-29 English text Ohio University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1091111473 http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1091111473 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Optimization Optimal Control Generalized Gradient Elliptic Equations |
| spellingShingle |
Optimization Optimal Control Generalized Gradient Elliptic Equations Voisei, Mircea D. First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| author |
Voisei, Mircea D. |
| author_facet |
Voisei, Mircea D. |
| author_sort |
Voisei, Mircea D. |
| title |
First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| title_short |
First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| title_full |
First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| title_fullStr |
First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| title_full_unstemmed |
First-Order Necessary Optimality Conditions for Nonlinear Optimal Control Problems |
| title_sort |
first-order necessary optimality conditions for nonlinear optimal control problems |
| publisher |
Ohio University / OhioLINK |
| publishDate |
2004 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1091111473 |
| work_keys_str_mv |
AT voiseimircead firstordernecessaryoptimalityconditionsfornonlinearoptimalcontrolproblems |
| _version_ |
1719424051290570752 |