EE609: Topics

• Linear algebra refresher

  • Vector norms and inner products

  • Projections onto subspaces

  • Vector functions and maps

  • Matrix norms

• Convexity fundamentals

  • Convex sets

  • Convex functions

  • Convex optimization problems and their structure

  • Optimality conditions

  • Duality, and its practical applications

• Linear, quadratic and geometric convex optimization problems

  • Convex sets

  • Unconstrained minimization of quadratic problems

  • Geometry of linear and convex quadratic inequalities

  • Linear and quadratic programs (QPs)

  • Modelling with linear and quadratic programs

  • Geometric programs (GP)

  • ML Application –regression and classification

  • Wireless Application – transmitter and receiver design, and power allocation

• Second order cone program (SOCP) and robust models

  • SOCP representable problems and examples

  • Robust optimization

  • Wireless application –transmitter design robust to user mobility

• Semidefinite programs (SDP)

  • From linear to conic models

  • Linear matrix inequalities

  • Semidefinite programs

  • Wireless application – low-complexity multi-antenna receiver design

• Fractional Programs (FP) and Quadratic Transform (QT)

  • FP and QT representable problems and examples

  • Wireless application: user scheduling problem in cellular systems

• Optimization algorithms

  • Algorithms for smooth unconstrained minimization

  • Algorithms for smooth convex constrained minimization

  • Convex optimization problems and their structure

  • Coordinate descent methods

  • ML application: Variational Inference (VI) and variational EM (VEM) algorithms

  • Decentralized optimization methods