Thesis (Ph.D.)--Bowling Green State University, 2005. / Document formatted into pages; contains v, 73 p. Includes bibliographical references.

This thesis focuses on optimization problems with generalized orthogonality constraints, which may also contains linear equality constraints. These problems appear in many areas, such as machine learning, signal processing, computer vision and so on.;Many problems in this form are NP hard. One challenge posed by generalized orthogonality constraints is local minimizers loaded by nonconvex constraints. More-over, the generalized orthogonality constraints are numerically expensive to preserve during iterations.;This thesis is mainly divided into two parts. The first part is focused on solving generalized orthogonality constrained optimization problems with differentiable objective functions. For this class of optimization problems, a generalized gradient.;This thesis is mainly divided into two parts. The first part is focused on solving generalized orthogonality constrained optimization problems with differentiable objective functions. For this class of optimization problems, a generalized gradient flow is proposed, which is contained on the constraints set if the initial condition satisfies generalized orthogonality constrains. The week convergence of the generalizedgradient flow is given. A discrete iterative scheme is also proposed to make the gradient flow method computable. In addition, we analyze the relationship between our discrete iteration scheme and some existing constraint preserving methods, and the relationship between our discrete iteration scheme and the inexact forward-backward method, respectively. Several problems which also can be solved by the generalized gradient flow are given. Furthermore, we also propose an optimal gradient flow by an alyzing the first order optimality condition.;The second part of this thesis is devoted to study of the generalized orthogonality constrained optimization problems with nondifferentiable objective functions. An approximate augmented Lagrangian method is used to deal with this class of problems. The global convergence is presented. We also extend the proximal alternating linearized minimization method (EPALM) to deal with the generalized orthogonality constraints appeared in the subproblem of the approximate augmented Lagrangian method. Moreover, to accelerate the EPALM method, an inertial proximal alternating linearized minimization method (IPALM) is proposed to deal with unconstrained nonconvex, nonsmooth problems with coupled objective functions.;Keywords: Generalized Orthogonality Constraints; Stiefel Manifold; Tangent Space;Gradient Flow; Approximate Augmented Lagrangian Method; Proximal Alternating Linearized Minimization Method.

Thesis (Ph. D.)--University of Florida, 2004. / Title from title page of source document. Document formatted into pages; contains 199 pages. Includes vita. Includes bibliographical references.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 125-129). Also available in electronic version. Access restricted to campus users.

Thesis (M.S. in Meteorology)--Naval Postgraduate School, March 1982. / Bibliography: l. 146-148. Also available online.

The ever increasing demand for fast and efficient broadband wireless communication services requires future broadband communication systems to provide a high data rate, robust performance and low complexity within the limited available electromagnetic spectrum. One of the identified, most-promising techniques to support high performance and high data rate communication for future wireless broadband services is the deployment of multi-input multi-output (MIMO) antenna systems with orthogonal frequency division multiplexing (OFDM). The combination of MIMO and OFDM techniques guarantees a much more reliable and robust transmission over a hostile wireless channel through coding over the space, time and frequency domains. In this thesis, two full-rate space-time coded OFDM systems are proposed. The first one, designed for two transmit antennas, is called extended super-orthogonal space-time trellis coded OFDM (ESOSTTC-OFDM), and is based on constellation rotation. The second one, called super-quasi-orthogonal space-time trellis coded OFDM (SQOSTTCOFDM), combines a quasi-orthogonal space-time block code with a trellis code to provide a full-rate code for four transmit antennas. The designed space-time coded MIMO-OFDM systems achieve a high diversity order with high coding gain by exploiting the diversity advantage of frequency-selective fading channels. Concatenated codes have been shown to be an effective technique of achieving reliable communication close to the Shannon limit, provided that there is sufficient available diversity. In a bid to improve the performance of the super orthogonal space-time trellis code (SOSTTC) in frequency selective fading channels, five distinct concatenated codes are proposed for MIMO-OFDM over frequency-selective fading channels in the second part of this thesis. Four of the coding schemes are based on the concatenation of convolutional coding, interleaving, and space-time coding, along multiple-transmitter diversity systems, while the fifth coding scheme is based on the concatenation of two space-time codes and interleaving. The proposed concatenated Super-Orthogonal Space-Time Turbo-Coded OFDM System I. B. Oluwafemi 2012 vii coding schemes in MIMO-OFDM systems achieve high diversity gain by exploiting available diversity resources of frequency-selective fading channels and achieve a high coding gain through concatenations by employing the turbo principle. Using computer software simulations, the performance of the concatenated SOSTTC-OFDM schemes is compared with those of concatenated space-time trellis codes and those of conventional SOSTTC-OFDM schemes in frequency-selective fading channels. Simulation results show that the concatenated SOSTTC-OFDM system outperformed the concatenated space-time trellis codes and the conventional SOSTTC-OFDM system under the various channel scenarios in terms of both diversity order and coding gain. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

Thesis (Ph.D.)--Auburn University, 2007. / Abstract. Includes bibliographic references (ℓ. 68)

Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p. 70-74)

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 63-66). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 163-171). Also available in electronic version. Access restricted to campus users.