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 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 |
| References |
EE364A - Convex Optimization I
Instructors: Professor Stephen Boyd. Handouts. Assignments. Exams. This course concentrates on recognizing and solving convex optimization problems that arise in engineering.
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