Theory and Applications of Stochastic First-order Methods for Large-scale Stochastic Convex Optimization

大规模随机凸优化的随机一阶方法的理论与应用

• 批准号: 1000347
• 负责人: Guanghui Lan
• 金额: $ 20万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-01 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1000347&HistoricalAwards=false
• 关键词: Theory; Applications; Stochastic; First; order

This grant provides funding to study efficient algorithms for solving stochastic and large-scale convex programming (CP) problems. The development of CP algorithms is now facing a few new challenges. First, the incorporation of uncertainty, and possibly dynamics, has considerably increased the difficulty of solving CP. Second, the size of CP problems arising from many emerging applications, such as statistical learning, far exceeds the capability of existing polynomial-time solvers. In this project, we will study a new and promising class of stochastic first-order methods for solving stochastic CP and establish their convergence and large-deviation properties. Moreover, using these stochastic methods as the driving-force, we aim at enhance our capability for solving extremely large-scale CP through the development of novel randomization schemes. Finally we will advance the optimization solvers for various statistical learning models which are crucial in order to transform data into knowledge in our information age. If successful, the results of this research will lead to algorithmic innovation for solving Large-scale and stochastic CP problems arising from diverse areas in logistics, finance, energy, medicine, defense and science. In green energy systems, stochastic programming models are used for long-term operations planning of hydro-thermal power systems to deal with the stochastic streamflows. In medicine, statistical learning techniques can be applied to diagnose breast cancer by utilizing characteristics of individual cells to discriminate benign from malignant breast lumps. These are just a few application examples of SP, large-scale CP and statistical learning problems to be studied in this research that will impact society. Additionally, this research will contribute to open research infrastructure in optimization through the development of CP-solver software. We will also engage students in our research efforts.

该补助金提供资金用于研究解决随机和大规模凸规划（CP）问题的有效算法。CP算法的发展现在面临着一些新的挑战。第一，不确定性和可能的动力学的结合，大大增加了解决CP的难度。其次，许多新兴应用（如统计学习）所产生的CP问题的规模远远超过了现有多项式时间求解器的能力。在这个项目中，我们将研究一类新的和有前途的随机一阶方法来解决随机CP，并建立其收敛性和大偏差性质。此外，使用这些随机方法作为驱动力，我们的目标是通过开发新的随机方案来提高我们解决超大规模CP的能力。最后，我们将推进各种统计学习模型的优化求解器，这些模型对于在信息时代将数据转化为知识至关重要。如果成功，这项研究的结果将导致算法创新，用于解决物流，金融，能源，医学，国防和科学等不同领域的大规模和随机CP问题。在绿色能源系统中，考虑到河流流量的随机性，采用随机规划模型进行水火电系统的长期运行规划。在医学上，统计学习技术可以应用于诊断乳腺癌，通过利用单个细胞的特征来区分良性和恶性乳腺肿块。这些只是SP，大规模CP和统计学习问题的几个应用实例，将在这项研究中研究，将影响社会。此外，这项研究将有助于开放的研究基础设施，通过开发的CP求解器软件的优化。我们还将让学生参与我们的研究工作。