Week 1 : Introduction to properties of Vectors, Norms, Positive Semi-Definite matrices, Gaussian Random Vectors
Week 2 : Introduction to Convex Optimization – Convex sets, Hyperplanes/ Half-spaces etc. Application: Power constraints in Wireless Systems
Week 3 : Convex/ Concave Functions, Examples, Conditions for Convexity. Application: Beamforming in Wireless Systems, Multi-User Wireless, Cognitive Radio Systems
Week 4 : Convex Optimization problems, Linear Program, Application: Power allocation in Multi-cell cooperative OFDM
Week 5 : QCQP, SOCP Problems, Application: Channel shortening for Wireless Equalization, Robust Beamforming in Wireless Systems
Week 6 : Duality Principle and KKT Framework for Optimization. Application: Water-filling power allocation,Optimization for MIMO Systems, OFDM Systems and MIMO-OFDM systems
Week 7 : Optimization for signal estimation, LS, WLS, Regularization. Application: Wireless channel estimation, Image Reconstruction-Deblurring
Week 8 : Application: Convex optimization for Machine Learning, Principal Component Analysis (PCA), Support Vector Machines
Week 9 : Application: Cooperative Communication, Optimal Power Allocation for cooperative Communication, Geometric Program
Week 10 : Application: Compressive Sensing, Sparse Signal Processing, OMP (Orthogonal Matching Pursuit), LASSO (Least Absolute Shrinkage and Selection Operator) for signal estimation
Week 11 : Application: Radar for target detection, Array Processing, MUSIC, MIMO-Radar Schemes for Enhanced Target Detection
Week 12 : Application: Convex optimization for Big Data Analytics, Recommender systems, User Rating Prediction, Optimization for Finance
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