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. Various topics will be covered in different areas such as; Wireless: MIMO/ OFDM systems, Beamforming, Cognitive Radio and Cooperative Communication; Signal Processing: Signal Estimation, Regularization, Image Reconstruction; Compressive Sensing: Sparse estimation, OMP, LASSO techniques; Machine Learning: Principal Component Analysis (PCA), Support Vector Machines (SVM); Big-Data: Recommender systems, User-rating prediction, Latent Factor Method; Finance: Financial models, Portfolio Optimization.The course is suitable for all UG/PG students and practicing engineers/ scientists/ managers from the diverse fields mentioned above and interested in learning about the novel cutting edge applications of modern optimization technology.
INTENDED AUDIENCE : -Students in Electrical Engineering, Electronics and Communication Engineering, Mathematics, Economics, Computer Science -Practicing engineers -Technical and Non-technical managers of Telecomm companies -Students preparing for Competitive Exams with focus on Wireless Communication, Signal Processing - Students pursuing projects or research in Optimization and Wireless Communication PREREQUISITES : Basic knowledge of Calculus, Probability, Matrices INDUSTRY SUPPORT : Most companies in Electronics, Communication and Signal Processing. Examples are Qualcomm, Broadcom, Intel, MediaTek, Samsung etc. Companies in Machine Learning, AI, Big-Data and Finance will also find the content useful
Week 1 : Introduction to properties of Vectors, Norms, Positive Semi-Definite matrices, Gaussian Random VectorsWeek 2 : Introduction to Convex Optimization – Convex sets, Hyperplanes/ Half-spaces etc. Application: Power constraints in Wireless SystemsWeek 3 : Convex/ Concave Functions, Examples, Conditions for Convexity. Application: Beamforming in Wireless Systems, Multi-User Wireless, Cognitive Radio SystemsWeek 4 : Convex Optimization problems, Linear Program, Application: Power allocation in Multi-cell cooperative OFDMWeek 5 : QCQP, SOCP Problems, Application: Channel shortening for Wireless Equalization, Robust Beamforming in Wireless SystemsWeek 6 : Duality Principle and KKT Framework for Optimization. Application: Water-filling power allocation,Optimization for MIMO Systems, OFDM Systems and MIMO-OFDM systemsWeek 7 : Optimization for signal estimation, LS, WLS, Regularization. Application: Wireless channel estimation, Image Reconstruction-DeblurringWeek 8 : Application: Convex optimization for Machine Learning, Principal Component Analysis (PCA), Support Vector MachinesWeek 9 : Application: Cooperative Communication, Optimal Power Allocation for cooperative Communication, Geometric ProgramWeek 10 : Application: Compressive Sensing, Sparse Signal Processing, OMP (Orthogonal Matching Pursuit), LASSO (Least Absolute Shrinkage and Selection Operator) for signal estimationWeek 11 : Application: Radar for target detection, Array Processing, MUSIC, MIMO-Radar Schemes for Enhanced Target DetectionWeek 12 : Application: Convex optimization for Big Data Analytics, Recommender systems, User Rating Prediction, Optimization for Finance