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September 25, 2023

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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 – Gram-Schmidt 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 Multi-antenna Wireless Communication Unlimited
    • Lecture 35 – Practical Application: Maximal Ratio Combiner for Wireless Systems Unlimited
    • Lecture 36 – Practical Application: Multi-antenna Beamforming with Interfering User Unlimited
    • Lecture 37 – Practical Application: Zero-Forcing 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: Multi-antenna 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 – Karush-Kuhn-Tucker (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: Min-Max 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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