Course  Convex Optimization I
Concentrates on recognizing and solving convex optimization problems that arise in engineering.Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Leastsquares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.Prerequisites: Good knowledge of linear algebra. Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.

Lecture 1  Introduction to Convex Optimization I

Lecture 2  Guest Lecturer; Jacob Mattingley

Lecture 3  Logistics

Lecture 4  Vector Composition

Lecture 5  Optimal And Locally Optimal Points

Lecture 6  (Generalized) LinearFractional Program

Lecture 7  Generalized Inequality Constraints

Lecture 8  Lagrangian

Lecture 9  Complementary Slackness

Lecture 10  Applications Section of Course

Lecture 11  Statistical Estimation

Lecture 12  Continue On Experiment Design

Lecture 13  Linear Discrimination (Cont.)

Lecture 14  LU Factorization (Cont.)

Lecture 15  Algorithm Section Of The Course

Lecture 16  Continue On Unconstrained Minimization

Lecture 17  Newton's Method (Cont.)

Lecture 18  Logarithmic Barrier

Lecture 19  InteriorPoint Methods (Cont.)