| Type of Document |
Dissertation |
| Author |
Li, Qingxia
|
| Author's Email Address |
qingxia@math.lsu.edu |
| URN |
etd-06232010-112745 |
| Title |
Optimal Control and Nonlinear Programming |
| Degree |
Doctor of Philosophy (Ph.D.) |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Wolenski, Peter |
Committee Chair |
| Lawson, Jimmie |
Committee Member |
| Perlis, Robert |
Committee Member |
| Shipman, Stephen |
Committee Member |
| Sundar, Padmanabhan |
Committee Member |
| Wei, Shuangqing |
Dean's Representative |
|
| Keywords |
- Value function
- Subgradient
- Set-valued mappings.
|
| Date of Defense |
2010-04-21 |
| Availability |
unrestricted |
Abstract
In this thesis, we have two distinct but related subjects: optimal control and nonlinear programming. In the first part of this thesis, we prove that the value function, propagated from initial or terminal costs, and constraints, in the form of a differential equation, satisfy a subgradient form of the Hamilton-Jacobi equation in which the Hamiltonian is measurable with respect to time. In the second part of this thesis, we first construct a concrete example to demonstrate conjugate duality theory in vector optimization as developed by Tanino. We also define the normal cones corresponding to Tanino's concept of the subgradient of a set valued mapping and derive some infimal convolution properties for convex set-valued mappings. Then we deduce necessary and sufficient conditions for maximizing an objective function with constraints subject to any convex, pointed and closed cone.
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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
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dissertation.pdf |
394.68 Kb |
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00:00:56 |
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