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EE364A - Convex Optimization I

EE364A: Convex Optimization I (Stanford Univ.). Taught by Professor Stephen Boyd, this course concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, 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. (from see.stanford.edu)

Lecture 04 - Quasiconvex Functions, Examples, Log-Concave and Log-Convex Functions


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Lecture 01 - Introduction
Lecture 02 - Guest Lecturer: Jacob Mattingley, Convex Sets and Their Applications
Lecture 03 - Logistics, Convex Functions, Examples
Lecture 04 - Quasiconvex Functions, Examples, Log-Concave and Log-Convex Functions
Lecture 05 - Optimal and Locally Optimal Points, Convex Optimization Problem, Quasiconvex Optimization
Lecture 06 - Linear-Fractional Program, Quadratic Program
Lecture 07 - Generalized Inequality Constraints, Semidefinite Program (SDP)
Lecture 08 - Lagrangian, Least-Norm Solution Of Linear Equations, Dual Problem, Weak and Strong Duality
Lecture 09 - Complementary Slackness, Karush-Kuhn-Tucker (KKT) Conditions, Sensitivity, Duality
Lecture 10 - Applications: Norm Approximation, Penalty Function Approximation, Least-Norm Problems, etc.
Lecture 11 - Statistical Estimation, Maximum Likelihood Estimation
Lecture 12 - Geometric Problems
Lecture 13 - Linear Discrimination, Nonlinear Discrimination, Numerical Linear Algebra Background
Lecture 14 - Numerical Linear Algebra Background, Factorizations
Lecture 15 - Algorithm - Unconstrained Minimization
Lecture 16 - Unconstrained Minimization (cont.), Equality Constrained Minimization
Lecture 17 - Equality Constrained Minimization (cont.), Interior-Point Methods
Lecture 18 - Logarithmic Barrier, Central Path, Barrier Method, Feasibility and Phase I Methods
Lecture 19 - Interior-Point Methods, Barrier Method (Review), Generalized Inequalities