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Applied Optimization for Wireless, Machine Learning, Big Data

Applied Optimization for Wireless, Machine Learning, Big Data. Instructor: Prof. Aditya K. Jagannatham, Department of Electrical Engineering, IIT Kanpur. This course is focused on developing the fundamental tools/ techniques in modern optimization as well as illustrating their applications in diverse fields such as Wireless Communication, Signal Processing, Machine Learning, Big Data and Finance. (from nptel.ac.in)

Lecture 67 - Application of KKT Condition: Optimal MIMO Power Allocation (Waterfilling)


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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.)