Summer Vacation Research Project 1: Numerical optimization methods for big data analytics The data revolution is reshaping science, technology and business. Large-scale distributed optimization is emerging as a key tool in extracting useful information from the deluge of data that arises in many areas of application. In this project you will explore optimization methods for big data that include the alternating direction method of multipliers (ADMM) and the stochastic gradient descent (SGD) method. Applications of interest include, for example, matrix and tensor decompositions that may be used to generate user recommendations for movie and music streaming. The optimization algorithms will first be explored in Matlab. Areas of study may include algorithmic convergence acceleration of the ADMM and SGD methods, or efficient distributed implementations in the Spark framework for big data analytics. Some relevant links: -http://arxiv.org/abs/1508.03110 -http://stanford.edu/~boyd/papers/admm_distr_stats.html -http://spark.apache.org/docs/latest/mllib-optimization.html Required: -major in computational/applied mathematics, computer science, or engineering -at least one course on numerical computing -interest in and experience with programming (any of Matlab, Python, C, Java, C++, Scala, Spark, ...) Duration: 6 weeks, starting in December or January Funding: fully funded =============================== Summer Vacation Research Project 1: Parallel computing in time for large-scale PDE simulation Numerical approximations of time-dependent partial differential equation (PDE) problems in three spatial dimensions often require very fine grid resolutions, and parallel computing can be employed to speed up the computations by subdividing the spatial domain over the available parallel processors. However, parallelization in space alone becomes inefficient on new generations of parallel computers where the number of parallel processors (or cores) is very large. In order to increase the concurrency and parallel efficiency, one can consider to carry out computations that iteratively improve the approximation at different time levels in a concurrent fashion. This approach is very attractive conceptually. In particular, multilevel

methods for parallel computing in time will be explored for model problem PDEs of parabolic and hyperbolic type. Relevant link: -http://computation.llnl.gov/project/parallel-time-integration/pubs/mgritPaper-2013-3.pdf Required: -major in computational/applied mathematics, computer science, or engineering -at least one course on numerical computing; a course on PDEs -experience with programming (any of Matlab, Python, C, Java, C++, MPI, ...) and interest in parallel computing Duration: 6 weeks, starting in December or January Funding: Subject to Funding by Monash University or the School of Mathematical Sciences ===============================