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Applied Optimization for Wireless, Machine Learning, Big Data. Instructor: Prof. Aditya K. Jagannatham, Department of Electrical Engineering, IIT Kanpur.
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Description
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 content
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- 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
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- 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 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 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 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 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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