In this thesis we investigate the design and complexity analysis of the algorithms to solve convex programming problems under inexact first-order information. In the first part of this thesis we focus on the general non-smooth convex minimization under a stochastic oracle. We start by introducing an important algorithmic advancement in this area, namely, the development of the mirror descent stochastic approximation algorithm. The main contribution is to develop a validation procedure for this algorithm applied to stochastic programming. In the second part of this thesis we consider the Stochastic Composite Optimizaiton (SCO) which covers smooth, non-smooth and stochastic convex optimization as certain special cases. Note that the optimization algorithms that can achieve this lower bound had never been developed. Our contribution in this topic mainly consists of the following aspects. Firstly, with a novel analysis, it is demonstrated that the simple RM-SA algorithm applied to the aforementioned problems exhibits the best known so far rate of convergence. Moreover, by adapting Nesterov's optimal method, we propose an accelerated SA, which can achieve, uniformly in dimension, the theoretically optimal rate of convergence for solving this class of problems. Finally, the significant advantages of the accelerated SA over the existing algorithms are illustrated in the context of solving a class of stochastic programming problems. In the last part of this work, we extend our attention to certain deterministic optimization techniques which operate on approximate first-order information for the dual problem. In particular, we establish, for the first time in the literature, the iteration-complexity for the inexact augmented Lagrangian (I-AL) methods applied to a special class of convex programming problems.

Thesis (Ph. D., Education)--University of Idaho, April 2007. / Major professor: Mary Gardiner. Includes bibliographical references (leaves 170-179). Also available online (PDF file) by subscription or by purchasing the individual file.

Thesis (Ph.D.)--Ohio University, June, 2008. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 166-178). Also available on the Internet.

Thesis (M. Ed.)--University of Hong Kong, 1987. / Includes bibliographical references (leaf 91-96).

Thesis (M. Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 107-113).

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 166-178). Also available on the Internet.

Thesis (Ph. D.)--Michigan State University. Dept. of Educational Administration, 2008. / Title from PDF t.p. (viewed on Aug. 20, 2009) Includes bibliographical references (p. 173-183). Also issued in print.

Thesis (Ed.D.)--University of West Florida, 2008. / Title from title page of source document. Document formatted into pages; contains 156 pages. Includes bibliographical references.

Thesis (M.Ed.)--University of Hong Kong, 1987. / Includes bibliographical references (leaves 91-96). Also available in print.