Electrical and Electronics Engineering

Introduction to mathematical optimization; nonlinear programming; convex optimization; aim and subjects of the course. Repetition of linear algebra, Convex sets and cones. Some general and important examples; operations that protect convexity, Convex functions, Some general and important examples; operations that protect convexity; approx-convex and log-convex functions. Convex optimization problems, linear and quadratic programs; Duality, Lagrange dual function and problem, Optimal conditions, Applications: convergence and fitting; magnitude convergence; The regularization; robust optimization, pplications: statistical estimation; maximum likelihood and maximum finite probability (MAP) estimation, Applications: geometric problems; projection; excessive volume ellipsoids; classification; locating and locating problems.

The aim of this course is to introduce the students the tools necessary to recognize convex optimization problems in various science and engineering applications. To present the basic theory and to gain a modeling perspective which may be useful especially in applications. The subjects of the course are convex sets, convex functions, optimization problems, linear and quadratic programs, semidefinite programming, optimal states and duality theory. Signal processing, control, numerical and analog circuits theory, statistics, mechanical engineering applications will be introduced. Students will gain high level programming experience.