Applied Optimization For Wireless, Machine Learning, Big Data

Lectures

Intro to properties of Vectors, Norms, Positive Semi-Definite matrices and Gaussian Random Vectors

1. Lec 01- Vectors and Matrices- Linear Independence and Rank Video
2. Lec 02 - Eigenvectors and Eigenvalues of Matrices and their Properties Video
3. Lec 03 - Positive Semidefinite (PSD) and Postive Definite (PD) Matrices and their Properties Video
4. Lec 04 - Inner Product Space and it's Properties: Linearity, Symmetry and Positive Semi-definite Video
5. Lec 05 - Inner Product Space and its Properties: Cauchy Schwarz Inequality Video
6. Lec 06 - Properties of Norm, Gaussian Elimination and Echleon form of matrix Video

Week 2

7. Lec 07- Gram Schmidt Orthogonalization Procedure Video
8. Lec 08- Null Space and Trace of Matrices Video
9. Lec 09- Eigenvalue Decomposition of Hermitian Matrices and Properties Video
10. Lec 10- Matrix Inversion Lemma (Woodbury identity) Video
11. Lec 11- Introduction to Convex Sets and Properties Video
12. Lec 12- Affine Set Examples and Application Video

Week 3 : Beamforming in Wireless Systems, Multi-User Wireless, Cognitive Radio Systems

13. Lec 13- Norm Ball and its Practical Applications Video
14. Lec 14- Ellipsoid and its Practical Applications Video
15. Lec 15- Norm Cone,Polyhedron and its Applications Video
16. Lec 16- Applications: Cooperative Cellular Transmission Video
17. Lec 17- Positive Semi Definite Cone And Positive Semi Definite (PSD) Matrices Video
18. Lec 18-Introduction to Affine functions and examples Video

Week 4 : Convex Optimization problems, Linear Program, Application: Power allocation in Multi-cell cooperative OFDM

19. Lecture 19-norm balls and Matrix properties:Trace,Determinant Video
20. Lecture 20-Inverse of a Positive Definite Matrix Video
21. Lecture 21-Example Problems: Property of Norms,Problems on Convex Sets Video
22. Lecture 22-Problems on Convex Sets(contd.) Video
23. Lecture 23-Introduction to Convex and Concave Functions Video
24. Lecture 24-Properties of Convex Functions with examples Video
25. Lec 25-Test for Convexity: Positive Semidefinite Hessian Matrix Video
26. Lec 26-Application: MIMO Receiver Design as a Least Squares Problem Video

Week 5: QCQP, SOCP Problems, Application: Channel shortening for Wireless Equalization, Robust Beamforming in Wireless…

27. Lec 27-Jensen's Inequality and Practical Application Video
28. Lec 28-Jensen's Inequality application Video
29. Lec 29 - Properties of Convex Functions Video
30. Lec 30 - Conjugate Function and Examples to prove Convexity of various Functions Video
31. Lec 31- Example problems: Operations preserving Convexity(log-sum, average) and Quasi Convexity Video
32. Lec 32-Example Problems: Verify Convexity, Quasi -Convexity and Quasi- Concavity of functions Video
33. Lec 33-Example Problems:Perspective function, Product of Convex functions and Pointwise Maximum is Convex Video

Week-6: Duality Principle and KKT Framework for Optimization, Application: Water-filling power allocation,…

34. Lec 34- Practical Application: Beamforming in Multi-antenna Wireless Communication Video
35. Lec 35 - Practical Application: Maximal Ratio Combiner for Wireless Systems Video
36. Lec 36- Practical Application: Multi-antenna Beamforming with Interfering User Video
37. Lec 37- Practical Application: Zero-Forcing (ZF) Beamforming with Interfering User Video
38. Lec 38- Practical Application: Robust Beamforming With Channel Uncertainity for Wireless Systems Video
39. Lec 39- Practical Application: Robust Beamformer Design for Wireless Systems Video
40. Lec 40 - Practical Application: Detailed Solution for Robust Beamformer Computation in Wireless Systems Text Video

Week-7:Optimization for signal estimation, LS, WLS, Regularization. Application: Wireless channel estimation, Image…

41. Lec 41- Linear modeling and Approximation Problems: Least Squares Video
42. Lec 42-Geometric Intuition for Least Squares Video
43. Lec 43- Practical Application: Multi antenna channel estimation Video
44. Lec 44- Practical Application:Image deblurring Video
45. Lec 45- Least Norm Signal Estimation Video
46. Lec 46- Regularization: Least Squares + Least Norm Video
47. Lec 47- Convex Optimization Problem representation: Canonical form, Epigraph form Video

Week 8 : Application: Convex optimization for Machine Learning, Principal Component Analysis (PCA), Support Vector…

48. Lec 48-Linear Program Practical Application: Base Station Co-operation Video
49. Lec 49- Stochastic Linear Program,Gaussian Uncertainty Video
50. Lec 50- Practical Application: Multiple Input Multiple Output (MIMO) Beamforming Video
51. Lec 51- Practical Application: Multiple Input Multiple Output (MIMO) Beamformer Design Video
52. Lec 52-Practical Application: Co-operative Communication, Overview and various Protocols used Video
53. Lec 53- Practical Application: Probability of Error Computation for Co-operative Communication Video
54. Lec 54- Practical Application:Optimal power allocation factor determination for Co-operative Communication Video

Week 9- Application: Cooperative Communication, Optimal Power Allocation for cooperative Communication, Geometric…

55. Lec 55- Practical Application: Compressive Sensing Video
56. Lec 56- Practical Application Video
57. Lec 57- Practical Application- Orthogonal Matching Pursuit (OMP) algorithm for Compressive Sensing Video
58. Lec 58- Example Problem: Orthogonal Matching Pursuit (OMP) algorithm Video
59. Lec 59- Practical Application : L1 norm minimization and regularization approach for Compressive Sensing Optimization problem Video
60. Lec 60- Practical Application of Machine Learning and Artificial Intelligence:Linear Classification, Overview and Motivation Video
61. Lec 61- Practical Application: Linear Classifier (Support Vector Machine) Design Video

Week 10- Application: Compressive Sensing, Sparse Signal Processing, OMP (Orthogonal Matching Pursuit), LASSO (Least…

62. Lec 62- Practical Application: Approximate Classifier Design Video
63. Lec 63- Concept of Duality Video
64. Lec 64-Relation between optimal value of Primal & Dual Problems, concepts of Duality gap and Strong Duality Video
65. Lec 65-Example problem on Strong Duality Video
66. Lec 66- Karush-Kuhn-Tucker(KKT) conditions Video
67. Lec 67- Application of KKT condition:Optimal MIMO power allocation(Waterfilling) Video

Week 11 : Application: Radar for target detection, Array Processing, MUSIC, MIMO-Radar Schemes for Enhanced Target…

68. Lec 68- Optimal MIMO Power allocation(Waterfilling)-II Video
69. Lec 69- Example problem on Optimal MIMO Power allocation(Waterfilling) Video
70. Lec 70- Linear objective with box constraints, Linear Programming Video
71. Lec 71- Example Problems II Video
72. Lec 72- Examples on Quadratic Optimization Video
73. Lec 73- Examples on Duality: Dual Norm, Dual of Linear Program(LP) Video

Week 12: Application: Convex optimization for Big Data Analytics, Recommender systems, User Rating Prediction and…

74. Lec 74- Examples on Duality: Min-Max problem, Analytic Centering Video
75. Lec 75- Semi Definite Program(SDP) and its application:MIMO symbol vector decoding Video
76. Lec 76- Application:SDP for MIMO Maximum Likelihood(ML) Detection Video
77. Lec 77- Introduction to big Data: Online Recommender System(Netflix) Video
78. Lec 78- Matrix Completion Problem in Big Data: Netflix-I Video
79. Lec 79- Matrix Completion Problem in Big Data: Netflix-II Video