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Lecture 29 of 79Week 5: QCQP, SOCP Problems, Application: Channel shortening for Wireless Equalization, Robust Beamforming in Wireless…

Lec 29 - Properties of Convex Functions

Prof. Aditya K. Jagannatham · IIT Kanpur

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Applied Optimization For Wireless, Machine Learning, Big Data, IIT Kanpur (at NPTEL)
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All the lectures

  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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