NOC:Applied Optimization for Wireless, Machine Learning, Big Data


Lecture 1 - Vectors and Matrices - Linear Independence and Rank


Lecture 2 - Eigenvectors and Eigenvalues of Matrices and their Properties


Lecture 3 - Positive Semidefinite (PSD) and Postive Definite (PD) Matrices and their Properties


Lecture 4 - Inner Product Space and it's Properties: Linearity, Symmetry and Positive Semi-definite


Lecture 5 - Inner Product Space and it's Properties: Cauchy Schwarz Inequality


Lecture 6 - Properties of Norm, Gaussian Elimination and Echleon form of matrix


Lecture 7 - Gram Schmidt Orthogonalization Procedure


Lecture 8 - Null Space and Trace of Matrices


Lecture 9 - Eigenvalue Decomposition of Hermitian Matrices and Properties


Lecture 10 - Matrix Inversion Lemma (Woodbury identity)


Lecture 11 - Introduction to Convex Sets and Properties


Lecture 12 - Affine Set Examples and Application


Lecture 13 - Norm Ball and its Practical Applications


Lecture 14 - Ellipsoid and its Practical Applications


Lecture 15 - Norm Cone,Polyhedron and its Applications


Lecture 16 - Applications: Cooperative Cellular Transmission


Lecture 17 - Positive Semi Definite Cone And Positive Semi Definite (PSD) Matrices


Lecture 18 - Introduction to Affine functions and examples


Lecture 19 - norm balls and Matrix properties:Trace,Determinant


Lecture 20 - Inverse of a Positive Definite Matrix


Lecture 21 - Example Problems: Property of Norms,Problems on Convex Sets


Lecture 22 - Problems on Convex Sets (Continued...)


Lecture 23 - Introduction to Convex and Concave Functions


Lecture 24 - Properties of Convex Functions with examples


Lecture 25 - Test for Convexity: Positive Semidefinite Hessian Matrix


Lecture 26 - Application: MIMO Receiver Design as a Least Squares Problem


Lecture 27 - Jensen's Inequality and Practical Application


Lecture 28 - Jensen's Inequality application


Lecture 29 - Properties of Convex Functions


Lecture 30 - Conjugate Function and Examples to prove Convexity of various Functions


Lecture 31 - Examples on Operations Preserving Convexity


Lecture 32 - Examples on Test for Convexity, Quasi-Convexity


Lecture 33 - Examples on Convex Functions


Lecture 34 - Practical Application: Beamforming in Multi-antenna Wireless Communication


Lecture 35 - Practical Application: Maximal Ratio Combiner for Wireless Systems


Lecture 36 - Practical Application: Multi-antenna Beamforming with Interfering User


Lecture 37 - Practical Application: Zero-Forcing (ZF) Beamforming with Interfering User


Lecture 38 - Practical Application: Robust Beamforming With Channel Uncertainity for Wireless Systems


Lecture 39 - Practical Application: Robust Beamformer Design for Wireless Systems


Lecture 40 - Practical Application: Detailed Solution for Robust Beamformer Computation in Wireless Systems Text


Lecture 41 - Linear modeling and Approximation Problems: Least Squares


Lecture 42 - Geometric Intuition for Least Squares


Lecture 43 - Practical Application: Multi antenna channel estimation


Lecture 44 - Practical Application:Image deblurring


Lecture 45 - Least Norm Signal Estimation


Lecture 46 - Regularization: Least Squares + Least Norm


Lecture 47 - Convex Optimization Problem representation: Canonical form, Epigraph form


Lecture 48 - Linear Program Practical Application: Base Station Co-operation


Lecture 49 - Stochastic Linear Program,Gaussian Uncertainty


Lecture 50 - Practical Application: Multiple Input Multiple Output (MIMO) Beamforming


Lecture 51 - Practical Application: Multiple Input Multiple Output (MIMO) Beamformer Design


Lecture 52 - Practical Application: Co-operative Communication, Overview and various Protocols used


Lecture 53 - Practical Application: Probability of Error Computation for Co-operative Communication


Lecture 54 - Practical Application:Optimal power allocation factor determination for Co-operative Communication


Lecture 55 - Practical Application: Compressive Sensing


Lecture 56 - Practical Application


Lecture 57 - Practical Application- Orthogonal Matching Pursuit (OMP) algorithm for Compressive Sensing


Lecture 58 - Example Problem: Orthogonal Matching Pursuit (OMP) algorithm


Lecture 59 - Practical Application : L1 norm minimization and regularization approach for Compressive Sensing Optimization problem


Lecture 60 - Practical Application of Machine Learning and Artificial Intelligence:Linear Classification, Overview and Motivation


Lecture 61 - Practical Application: Linear Classifier (Support Vector Machine) Design


Lecture 62 - Practical Application: Approximate Classifier Design


Lecture 63 - Concept of Duality


Lecture 64 - Relation between optimal value of Primal and Dual Problems, concepts of Duality gap and Strong Duality


Lecture 65 - Example problem on Strong Duality


Lecture 66 - Karush-Kuhn-Tucker (KKT) conditions


Lecture 67 - Application of KKT condition:Optimal MIMO power allocation (Waterfilling)


Lecture 68 - Optimal MIMO Power allocation (Waterfilling)-II


Lecture 69 - Example problem on Optimal MIMO Power allocation (Waterfilling)


Lecture 70 - Linear objective with box constraints, Linear Programming


Lecture 71 - Example Problems II


Lecture 72 - Examples on Quadratic Optimization


Lecture 73 - Examples on Duality: Dual Norm, Dual of Linear Program (LP)


Lecture 74 - Examples on Duality: Min-Max problem, Analytic Centering


Lecture 75 - Semi Definite Program (SDP) and its application:MIMO symbol vector decoding


Lecture 76 - Application:SDP for MIMO Maximum Likelihood (ML) Detection


Lecture 77 - Introduction to big Data: Online Recommender System (Netflix)


Lecture 78 - Matrix Completion Problem in Big Data: Netflix-I


Lecture 79 - Matrix Completion Problem in Big Data: Netflix-II