The prevalence of high-dimensional data has motivated active research on efficient methods for tackling optimization problems that arise in statistical analysis. In this course, we will give an introduction to this exciting area of research, with emphasis on the theory of structured regularizers for high-dimensional statistics and the design and analysis of statistically and computationally efficient optimization algorithms. Applications in various areas of science and engineering, such as machine learning, signal processing, and statistics, will also be discussed. Students are expected to have taken ENGG 5501 or equivalent.