Browsing by Subject "Stochastic optimization"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Non-Convex Phase Retrieval Algorithms and Performance Analysis
    (2018-04) Wang, Gang
    High-dimensional signal estimation plays a fundamental role in various science and engineering applications, including optical and medical imaging, wireless communications, and power system monitoring. The ability to devise solution procedures that maintain high computational and statistical efficiency will facilitate increasing the resolution and speed of lensless imaging, identifying artifacts in products intended for military or national security, as well as protecting critical infrastructure including the smart power grid. This thesis contributes in both theory and methods to the fundamental problem of phase retrieval of high-dimensional (sparse) signals from magnitude-only measurements. Our vision is to leverage exciting advances in non-convex optimization and statistical learning to devise algorithmic tools that are simple, scalable, and easy-to-implement, while being computationally and statistically (near-)optimal. Phase retrieval is approached from a non-convex optimization perspective. To gain statistical and computational efficiency, the magnitude data (instead of the intensities) are fitted based on the least-squares or maximum likelihood criterion, which leads to optimization models that trade off smoothness for ‘low-order’ non-convexity. To solve the resultant challenging nonconvex and non-smooth optimization, the present thesis introduces a two-stage algorithmic framework, that is termed amplitude flow. The amplitude flows start with a careful initialization, which is subsequently refined by a sequence of regularized gradient-type iterations. Both stages are lightweight, and they scale well with problem dimensions. Due to the highly non-convex landscape, judicious gradient regularization techniques such as trimming (i.e., truncation) and iterative reweighting are devised to boost the exact phase recovery performance. It is shown that successive iterates of the amplitude flows provably converge to the global optimum at a geometric rate, corroborating their efficiency in terms of computational, storage, and data resources. The amplitude flows are also demonstrated to be stable vis-a-vis additive noise. Sparsity plays a instrumental role in many scientific fields - what has led to the upsurge of research referred to as compressive sampling. In diverse applications, the signal is naturally sparse or admits a sparse representation after some known and deterministic linear transformation. This thesis also accounts for phase retrieval of sparse signals, by putting forth sparsity-cognizant amplitude flow variants. Although analysis, comparisons, and corroborating tests focus on non-convex phase retrieval in this thesis, a succinct overview of other areas is provided to highlight the universality of the novel algorithmic framework to a number of intriguing future research directions.
  • Thumbnail Image
    Item
    Resource Allocation for Green Cloud Networks under Uncertainty: Stochastic, Robust and Big Data-driven Approaches
    (2016-09) CHEN, TIANYI
    Major improvements have propelled the development of worldwide Internet systems during the past decade. To meet the growing demand in massive data processing, a large number of geographically-distributed data centers begin to surge in the era of data deluge and information explosion. Along with their remarkable expansion, contemporary cloud networks are being challenged by the growing concerns about global warming, due to their substantial energy consumption. Hence, the infrastructure of future data centers must be energy-efficient and sustainable. Fortunately, supporting technologies of smart grids, big data analytics and machine learning, are also developing rapidly. These considerations motivate well the present thesis, which mainly focuses on developing interdisciplinary approaches to offer sustainable resource allocation for future cloud networks, by leveraging three intertwining research subjects. The modern smart grid has many new features and advanced capabilities including e.g., high penetration of renewable energy sources, and dynamic pricing based demand-side management. Clearly, by integrating these features into the cloud network infrastructure, it becomes feasible to realize its desiderata of reliability, energy-efficiency and sustainability. Yet, full benefits of the renewable energy (e.g., wind and solar) can only be harnessed by properly mitigating its intrinsically stochastic nature, which is still a challenging task. This prompts leveraging the huge volume of historical data to reduce the stochasticity of online decision making. Specifically, valuable insights from big data analytics can enable a markedly improved resource allocation policy by learning historical user and environmental patterns. Relevant machine learning approaches can further uncover “hidden insights” from historical relationships and trends in massive datasets. Targeting this goal, the present thesis systematically studies resource allocation tasks for future sustainable cloud networks under uncertainty. With an eye towards realistic scenarios, the thesis progressively adapts elegant mathematical models, optimization frameworks, and develops low complexity algorithms from three different aspects: stochastic (Chapters 2 and 3), robust (Chapter 4), and big data-driven approaches (Chapter 5). The resultant algorithms are all numerically efficient with optimality guarantees, and most of them are also amenable to a distributed implementation.
  • Thumbnail Image
    Item
    Resource management in wireless heterogeneous networks: an optimization perspective
    (2014-12) Sanjabi Boroujeni, Maziar
    In this dissertation we consider the central task of resource management in wireless Heterogeneous Networks (HetNets). Resource management plays an important role in satisfying the increasing need for wireless data in HetNets. Our emphasis is mainly on cross layer strategies. Various aspects of cross layer resource management can be formulated as optimization problems. Throughout this dissertation, we use advanced optimization techniques to develop algorithms that are capable of efficiently solving these optimization problems. First, we consider the joint base station assignment and linear {transceiver} design problem. In order to gain a better understanding of resource management problems, we analyze the complexity of solving the resulting optimization problem. We establish the NP-hardness of this problem for a wide range of system-wide utility functions.Due to the fundamental difficulty of globally solving these problems, our emphasis in the rest of this dissertation is on devising efficient algorithms that can approximately solve these problems under different practical limitations. One major practical limitation of current resource management strategies is the need for the channel state information at the transmitter side. In this thesis we consider transceiver design in wireless HetNet when the channel state information is incomplete/inexact. We propose a general stochastic successive upper-bound minimization approach to optimize the average/ergodic utility of the system. We specialize our method to obtain an efficient stochastic sum-rate maximization algorithm. The proposed algorithm can use the statistical knowledge instead of actual channel values and is guaranteed to converge to the set of stationary points of the stochastic sum-rate maximization problem. We further generalize our stochastic method to a cross layer framework for jointly optimizing the base station clustering and the downlink beamformers in a partial coordinated transmission scenario. The partial coordination is crucial in improving the overall system performance by reducing backhaul overhead. We validate the effectiveness of our methods via numerical experiments.