Thesis (Ph. D.)--University of Washington, 1990. / Vita. Includes bibliographical references (leaves [97]-100).

Thesis (Ph. D.)--University of Chicago, Graduate School of Business, December 2000. / Includes bibliographical references. Also available on the Internet.

Diss.: Berlin, Humboldt-University, 2009. / Includes bibliographical references (p. 159-168).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: S. Joe Qin. Vita. Includes bibliographical references.

In the literature, error bound conditions have been widely used for studying the linear convergence rates of various first-order algorithms and the majority of literature focuses on how to sufficiently ensure these error bound conditions, usually posing more assumptions on the model under discussion. In this thesis, we focus on the alternating direction method of multipliers (ADMM), and show that the known error bound conditions for studying ADMM's linear convergence, can indeed be further weakened if the error bound is studied over the specific iterative sequence generated by ADMM. A so-called partial error bound condition, which is tailored for the specific ADMM's iterative scheme and weaker than known error bound conditions in the literature, is thus proposed to derive the linear convergence of ADMM. We further show that this partial error bound condition theoretically justifies the difference if the two primal variables are updated in different orders in implementing ADMM, which had been empirically observed in the literature yet no theory is known so far.

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Nemhauser, George; Committee Co-Chair: Ahmed, Shabbir; Committee Member: Bill Cook; Committee Member: Gu, Zonghao; Committee Member: Johnson, Ellis. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Arizona, 2005. / Includes bibliographical references (leaves 98-104). Also available online.

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Lee, Eva K.; Committee Member: Barnes, Earl; Committee Member: Hertel, Nolan E.; Committee Member: Johnson, Ellis; Committee Member: Monteiro, Renato D.C.

Thesis (M.S.)--Ohio University, August, 2004. / Includes bibliographical references (p. 64-66).

Thesis (Ph.D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Ozlem Ergun; Committee Member: Dana Randall; Committee Member: Joel Sokol; Committee Member: Shabbir Ahmed; Committee Member: William Cook.