Doctor of Philosophy (PhD)
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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Li, Qingxia, "Optimal control and nonlinear programming" (2010). LSU Doctoral Dissertations. 3545.