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Type of Document Dissertation Author Mouktonglang, Thanasak Author's Email Address tmoukton@nd.edu URN etd-05282004-122205 Title Numerical Implementation of a Class of Infinite-Dimensional Primal-Dual Algorithms Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Leonid Faybusovich Committee Chair Keywords
- second order cone programming
- Optimization
- linear-quadratic control
Date of Defense 2004-04-20 Availability unrestricted Abstract This Thesis is devoted to primal-dual algorithms in theinfinite-dimensional setting. We consider a class of
infinite-dimensional optimization problems and its applications to
optimal control problems. A primal-dual algorithm based on
Nesterov-Todd direction is implemented. We apply this algorithm
to two important control problems: multi-criteria
linear-quadratic control problems and linear-quadratic control
problems with quadratic constraints. Numerical experiments
confirm very fast convergence of the algorithm which is predicted
by the theory based on the concept of infinite-dimensional Jordan
algebras. Necessary theoretical results have been developed. To
the best of our knowledge this is the first implementation of this
class of algorithms.
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