Convex optimization theory with applications in signal processing, finance, and machine learning. It covers fundamentals (convex sets/functions/problems, Lagrange duality, algorithms), more advanced optimization techniques (sparsity, low-rank, robust optimization, decomposition methods, distributed algorithms), and specific applications (e.g., portfolio optimization, filter/beamforming design, classification methods, wireless communication systems, circuit design, image processing, data-drived graph learning, discrete MLE, network optimization, Internet protocol design, etc.).For PG students in second year or above.