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Last updated:
September 25, 2023
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
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)
Course Curriculum

 Lecture 01 – Vectors and Matrices – Linear Independence and Rank Unlimited
 Lecture 02 – Eigenvectors and Eigenvalues of Matrices and their Properties Unlimited
 Lecture 03 – Positive Semidefinite Matrices and Positive Definite Matrices Unlimited
 Lecture 04 – Inner Product Space and its Properties: Linearity, Symmetry and … Unlimited
 Lecture 05 – Inner Product Space and its Properties: Cauchy Schwarz Inequality Unlimited
 Lecture 06 – Properties of Norm, Gaussian Elimination and Echelon Form of Matrix Unlimited
 Lecture 07 – GramSchmidt Orthogonalization Procedure Unlimited
 Lecture 08 – Null Space and Trace of Matrices Unlimited
 Lecture 09 – Eigenvalue Decomposition of Hermitian Matrices and Properties Unlimited
 Lecture 10 – Matrix Inversion Lemma (Woodbury Identity) Unlimited
 Lecture 11 – Introduction to Convex Sets and Properties Unlimited
 Lecture 12 – Affine Set Examples and Application Unlimited

 Lecture 13 – Norm Ball and its Practical Applications Unlimited
 Lecture 14 – Ellipsoid and its Practical Applications Unlimited
 Lecture 15 – Norm Cone, Polyhedron and its Applications Unlimited
 Lecture 16 – Applications: Cooperative Cellular Transmission Unlimited
 Lecture 17 – Positive Semidefinite Cone and Positive Semidefinite Matrices Unlimited
 Lecture 18 – Introduction to Affine Functions and Examples Unlimited

 Lecture 19 – Norm Balls and Matrix Properties: Trace, Determinant Unlimited
 Lecture 20 – Inverse of a Positive Definite Matrix Unlimited
 Lecture 21 – Example Problems: Property of Norms, Problems on Convex Sets Unlimited
 Lecture 22 – Problems on Convex Sets (cont.) Unlimited
 Lecture 23 – Introduction to Convex and Concave Functions Unlimited
 Lecture 24 – Properties of Convex Functions with Examples Unlimited
 Lecture 25 – Test for Convexity: Positive Semidefinite Hessian Matrix Unlimited
 Lecture 26 – Application: MIMO Receiver Design as a Least Squares Problem Unlimited

 Lecture 27 – Jensen’s Inequality and Practical Application Unlimited
 Lecture 28 – Jensen’s Inequality Application Unlimited
 Lecture 29 – Properties of Convex Functions Unlimited
 Lecture 30 – Conjugate Function and Examples to Prove Convexity of Various Functions Unlimited
 Lecture 31 – Example Problems: Operations Preserving Convexity and Quasi Convexity Unlimited
 Lecture 32 – Example Problems: Verify Convexity, Quasi Convexity and … Unlimited
 Lecture 33 – Example Problems: Perspective Function, Product of Convex Functions Unlimited

 Lecture 34 – Practical Application: Beamforming in Multiantenna Wireless Communication Unlimited
 Lecture 35 – Practical Application: Maximal Ratio Combiner for Wireless Systems Unlimited
 Lecture 36 – Practical Application: Multiantenna Beamforming with Interfering User Unlimited
 Lecture 37 – Practical Application: ZeroForcing Beamforming with Interfering User Unlimited
 Lecture 38 – Practical Application: Robust Beamforming with Channel Uncertainty … Unlimited
 Lecture 39 – Practical Application: Robust Beamformer Design for Wireless Systems Unlimited
 Lecture 40 – Practical Application: Detailed Solution for Robust Beamformer Computation Unlimited

 Lecture 41 – Linear Modeling and Approximation Problems: Least Squares Unlimited
 Lecture 42 – Geometric Intuition for Least Squares Unlimited
 Lecture 43 – Practical Application: Multiantenna Channel Estimation Unlimited
 Lecture 44 – Practical Application: Image Deblurring Unlimited
 Lecture 45 – Least Norm Signal Estimation Unlimited
 Lecture 46 – Regularization: Least Squares + Least Norm Unlimited
 Lecture 47 – Convex Optimization Problem Representation: Canonical Form, Epigraph Form Unlimited

 Lecture 48 – Linear Program Practical Application: Base Station Cooperation Unlimited
 Lecture 49 – Stochastic Linear Program, Gaussian Uncertainty Unlimited
 Lecture 50 – Practical Application: Multiple Input Multiple Output Beamforming Unlimited
 Lecture 51 – Practical Application: Multiple Input Multiple Output Beamformer Design Unlimited
 Lecture 52 – Practical Application: Cooperative Communication, … Unlimited
 Lecture 53 – Practical Application: Probability of Error Computation for … Unlimited
 Lecture 54 – Practical Application: Optimal Power Allocation Factor Determination for Cooperative Communication Unlimited

 Lecture 55 – Practical Application: Compressive Sensing Unlimited
 Lecture 56 – Practical Application: Compressive Sensing (cont.) Unlimited
 Lecture 57 – Practical Application: Orthogonal Matching Pursuit Algorithm for Compressive Sensing Unlimited
 Lecture 58 – Example Problem: Orthogonal Matching Pursuit Algorithm Unlimited
 Lecture 59 – Practical Application: L1 Norm Minimization and … Unlimited
 Lecture 60 – Practical Application of Machine Learning and Artificial Intelligence Unlimited
 Lecture 61 – Practical Application: Linear Classifier (Support Vector Machine) Design Unlimited

 Lecture 62 – Practical Application: Approximate Classifier Design Unlimited
 Lecture 63 – Concept of Duality Unlimited
 Lecture 64 – Relation between Optimal Value of Primal and Dual Problems, … Unlimited
 Lecture 65 – Example Problem on Strong Duality Unlimited
 Lecture 66 – KarushKuhnTucker (KKT) Conditions Unlimited
 Lecture 67 – Application of KKT Condition: Optimal MIMO Power Allocation (Waterfilling) Unlimited

 Lecture 68 – Application: Optimal MIMO Power Allocation (Waterfilling) (cont.) Unlimited
 Lecture 69 – Example Problem on Optimal MIMO Power Allocation (Waterfilling) Unlimited
 Lecture 70 – Linear Objective with Box Constraints, Linear Programming Unlimited
 Lecture 71 – Example Problems on Convex Optimization Unlimited
 Lecture 72 – Examples on Quadratic Optimization Unlimited
 Lecture 73 – Examples on Duality: Dual Norm, Dual of Linear Program Unlimited

 Lecture 74 – Examples on Duality: MinMax Problem, Analytic Centering Unlimited
 Lecture 75 – Semidefinite Program and its Application: MIMO Symbol Vector Decoding Unlimited
 Lecture 76 – Application: SDP for MIMO Maximum Likelihood Detection Unlimited
 Lecture 77 – Introduction to Big Data: Online Recommender System (Netflix) Unlimited
 Lecture 78 – Matrix Completion Problem in Big Data: Netflix Unlimited
 Lecture 79 – Matrix Completion Problem in Big Data: Netflix (cont.) Unlimited
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