# InfoCoBuild

### 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)

 Introduction

 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.)

 References 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.