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

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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.