Here, I summarizes some self-learning and reference materials that I found very useful for my research:
  • Optimization
  1. Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course. [Link]
  2. Boyd and Vandenberghe, Convex Optimization. [Link]
  3. J. Nocedal, S. Wright, Numerical Optimization. [Link][Course Link]
  4. D. P. Bertsekas, Nonlinear Programming. [Link]
  • Function and Matrix Analysis
  1. R. Vershynin, Lectures in Functional Analysis. [Link]
  2. J. Hunter, B. Nachtergaele, Applied Analysis. [Link]
  3. R. A. Horn, C. R. Johnson, Matrix Analysis. [Link]
  4. G. H. Golub, and C. F. Van Loan, Matrix Computations. [Link]
  • Concentration Inequality and Random Matrix Theory
  1. R. V. Handel, Probability in High Dimensions. [Link]
  2. S. Boucheron, G. Lugosi, P. Massart, Concentration Inequalities: A Non-Asymptotic Theory of Independence. [Link]
  3. J. Tropp, An Introduction to Matrix Concentration Inequalities. [Link]
  4. R. Vershynin, Introduction to the Non-Asymptotic Analysis of Random Matrices. [Link]
  • Compressed Sensing
  1. S. Foucart, H. Rauhut, A Mathematical Introduction to Compressed Sensing. [Link]
  2. E. Candes, Compressed Sensing LMS Series 2011. [Link]
  3. Nuit Blanche. [Link]
  • High Dimensional Geometry and Differential Manifold
  1. R. Vershynin, Estimation in high dimensions: a geometric perspective. [Link]
  2. J. Matousek, Lectures on Discrete Geometry. [Link]
  3. J. M. Lee, Introduction to Smooth Manifold. [Link]
  4. P.-A. Absil, R. Mahony, R. Sepulchre, Optimization Algorithms on Matrix Manifolds. [Link]
  • Machine Learning
  1. D. Hsu, Advanced Machine Learning. [Link]
  2. A. Moitra, Algorithmic Aspects of Machine Learning. [Link]