| Introduction to Properties of Vectors, Norms, Positive Semi-definite Matrices |
| Lecture 01 - Vectors and Matrices - Linear Independence and Rank |
| Lecture 02 - Eigenvectors and Eigenvalues of Matrices and their Properties |
| Lecture 03 - Positive Semidefinite Matrices and Positive Definite Matrices |
| Lecture 04 - Inner Product Space and its Properties: Linearity, Symmetry and Positive Semidefinite |
| Lecture 05 - Inner Product Space and its Properties: Cauchy Schwarz Inequality |
| Lecture 06 - Properties of Norm, Gaussian Elimination and Echelon Form of Matrix |
| Lecture 07 - Gram-Schmidt Orthogonalization Procedure |
| Lecture 08 - Null Space and Trace of Matrices |
| Lecture 09 - 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 |
| Beaming Forming in Wireless Systems, Multi-user Wireless, Cognitive Radio Systems |
| 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 Semidefinite Cone and Positive Semidefinite Matrices |
| Lecture 18 - Introduction to Affine Functions and Examples |
| Convex Optimization Problems, Linear Program |
| 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 (cont.) |
| 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 |
| QCQP, SOCP Problems, Applications |
| 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 - Example Problems: Operations Preserving Convexity and Quasi Convexity |
| Lecture 32 - Example Problems: Verify Convexity, Quasi Convexity and Quasi Concavity of Functions |
| Lecture 33 - Example Problems: Perspective Function, Product of Convex Functions |
| Duality Principle and KKT Framework for Optimization, Application |
| 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 Beamforming with Interfering User |
| Lecture 38 - Practical Application: Robust Beamforming with Channel Uncertainty for Wireless Systems |
| Lecture 39 - Practical Application: Robust Beamformer Design for Wireless Systems |
| Lecture 40 - Practical Application: Detailed Solution for Robust Beamformer Computation |
| Optimization for Signal Estimation, LS, WLS, Regularization, Application |
| 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 |
| Application: Convex Optimization for Machine Learning, Principal Component Analysis, Support Vector Machines |
| Lecture 48 - Linear Program Practical Application: Base Station Cooperation |
| Lecture 49 - Stochastic Linear Program, Gaussian Uncertainty |
| Lecture 50 - Practical Application: Multiple Input Multiple Output Beamforming |
| Lecture 51 - Practical Application: Multiple Input Multiple Output Beamformer Design |
| Lecture 52 - Practical Application: Cooperative Communication, Overview and Various Protocols Used |
| Lecture 53 - Practical Application: Probability of Error Computation for Cooperative Communication |
| Lecture 54 - Practical Application: Optimal Power Allocation Factor Determination for Cooperative Communication |
| Application: Compressive Sensing |
| Lecture 55 - Practical Application: Compressive Sensing |
| Lecture 56 - Practical Application: Compressive Sensing (cont.) |
| Lecture 57 - Practical Application: Orthogonal Matching Pursuit Algorithm for Compressive Sensing |
| Lecture 58 - Example Problem: Orthogonal Matching Pursuit 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 |
| Lecture 61 - Practical Application: Linear Classifier (Support Vector Machine) Design |
| Practical Application: Approximate Classifier |
| 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) |
| Application: Optimal MIMO Power Allocation |
| Lecture 68 - Application: Optimal MIMO Power Allocation (Waterfilling) (cont.) |
| Lecture 69 - Example Problem on Optimal MIMO Power Allocation (Waterfilling) |
| Lecture 70 - Linear Objective with Box Constraints, Linear Programming |
| Lecture 71 - Example Problems on Convex Optimization |
| Lecture 72 - Examples on Quadratic Optimization |
| Lecture 73 - Examples on Duality: Dual Norm, Dual of Linear Program |
| Application: Convex Optimization for Big Data Analytics |
| Lecture 74 - Examples on Duality: Min-Max Problem, Analytic Centering |
| Lecture 75 - Semidefinite Program and its Application: MIMO Symbol Vector Decoding |
| Lecture 76 - Application: SDP for MIMO Maximum Likelihood Detection |
| Lecture 77 - Introduction to Big Data: Online Recommender System (Netflix) |
| Lecture 78 - Matrix Completion Problem in Big Data: Netflix |
| Lecture 79 - Matrix Completion Problem in Big Data: Netflix (cont.) |