Thesis--Rheinische Friedrich-Wilhelms-Universität zu Bonn. / Text in English; thesis statement and introd. in German. Includes bibliographical references (p. 93-96).

Thesis (M.S.)--Ohio University, June, 2005. / Title from PDF t.p. Includes bibliographical references (p. 90-92)

Sparse and low-rank models have been becoming fundamental machine learning tools and have wide applications in areas including computer vision, data mining, bioinformatics and so on. It is of vital importance, yet of great difficulty, to develop efficient optimization algorithms for solving these models, especially under practical design considerations of computational, communicational and privacy restrictions for ever-growing larger scale problems. This thesis proposes a set of new algorithms to improve the efficiency of the sparse and low-rank models optimization. First, facing a large number of data samples during training of empirical risk minimization (ERM) with structured sparse regularization, the gradient computation part of the optimization can be computationally expensive and becomes the bottleneck. Therefore, I propose two gradient efficient optimization algorithms to reduce the total or per-iteration computational cost of the gradient evaluation step, which are new variants of the widely used generalized conditional gradient (GCG) method and incremental proximal gradient (PG) method, correspondingly. In detail, I propose a novel algorithm under GCG framework that requires optimal count of gradient evaluations as proximal gradient. I also propose a refined variant for a type of gauge regularized problem, where approximation techniques are allowed to further accelerate linear subproblem computation. Moreover, under the incremental proximal gradient framework, I propose to approximate the composite penalty by its proximal average under incremental gradient framework, so that a trade-off is made between precision and efficiency. Theoretical analysis and empirical studies show the efficiency of the proposed methods. Furthermore, the large data dimension (e.g. the large frame size of high-resolution image and video data) can lead to high per-iteration computational complexity, thus results into poor-scalability of the optimization algorithm from practical perspective. In particular, in spectral k-support norm regularized robust low-rank matrix and tensor optimization, traditional proximal map based alternating direction method of multipliers (ADMM) requires to evaluate a super-linear complexity subproblem in each iteration. I propose a set of per-iteration computational efficient alternatives to reduce the cost to linear and nearly linear with respect to the input data dimension for matrix and tensor case, correspondingly. The proposed algorithms consider the dual objective of the original problem that can take advantage of the more computational efficient linear oracle of the spectral k-support norm to be evaluated. Further, by studying the sub-gradient of the loss of the dual objective, a line-search strategy is adopted in the algorithm to enable it to adapt to the Holder smoothness. The overall convergence rate is also provided. Experiments on various computer vision and image processing applications demonstrate the superior prediction performance and computation efficiency of the proposed algorithm. In addition, since machine learning datasets often contain sensitive individual information, privacy-preserving becomes more and more important during sparse optimization. I provide two differentially private optimization algorithms under two common large-scale machine learning computing contexts, i.e., distributed and streaming optimization, correspondingly. For the distributed setting, I develop a new algorithm with 1) guaranteed strict differential privacy requirement, 2) nearly optimal utility and 3) reduced uplink communication complexity, for a nearly unexplored context with features partitioned among different parties under privacy restriction. For the streaming setting, I propose to improve the utility of the private algorithm by trading the privacy of distant input instances, under the differential privacy restriction. I show that the proposed method can either solve the private approximation function by a projected gradient update for projection-friendly constraints, or by a conditional gradient step for linear oracle-friendly constraint, both of which improve the regret bound to match the nonprivate optimal counterpart.

An electricity market is very complex and different in its nature, when compared to other commodity markets. The introduction of competition and restructuring in global electricity markets brought more complexity and major changes in terms of governance, ownership and technical and market operations. In a liberalized electricity market, all market participants are responsible for their own decisions; therefore, all the participants are trying to make profit by participating in electricity trading. There are different types of electricity market, and in this research a bilateral electricity market has been specifically considered. This thesis not only contributes with regard to the reviewing UK electricity market as an example of a bilateral electricity market with more than 97% of long-term bilateral trading, but also proposes a dual aspect point of view with regard to the bilateral electricity market by splitting the generation and supply sides of the wholesale market. This research aims at maximizing the market participants’ profits and finds the equilibrium point of the bilateral market; hence, various methods such as equilibrium models have been reviewed with regard to management of the risks (e.g. technical and financial risks) of participating in the electricity market. This research proposes a novel Conjectural Variation Equilibrium (CVE) model for bilateral electricity markets, to reduce the market participants’ exposure to risks and maximize the profits. Hence, generation companies’ behaviors and strategies in an imperfect bilateral market environment, oligopoly, have been investigated by applying the CVE method. By looking at the bilateral market from an alternative aspect, the supply companies’ behaviors in an oligopsony environment have also been taken into consideration. At the final stage of this research, the ‘matching’ of both quantity and price between oligopolistic and oligopsonistic markets has been obtained through a novel-coordinating algorithm that includes CVE model iterations of both markets. Such matching can be achieved by adopting a hierarchical optimization approach, using the Matlab Patternsearch optimization algorithm, which acts as a virtual broker to find the equilibrium point of both markets. Index Terms-- Bilateral electricity market, Oligopolistic market, Oligopsonistic market, Conjectural Variation Equilibrium method, Patternsearch optimization, Game theory, Hierarchical optimization method

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 67-72).

Thesis (Ph. D.)--Worcester Polytechnic Institute. / Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2005. / Paul Griffin, Committee Member ; Kwok-Leung Tsui, Committee Chair ; Christos Alexopoulos, Committee Co-Chair ; Hengqing Ye, Committee Co-Chair ; David Goldsman, Committee Member. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 48-49). Also available on the Internet.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 48-49). Also available on the Internet.