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Stanford Engineering

Convex Optimization I

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 )

Instructor

Professor Stephen Boyd.
Electronics
2008

Record ID

recQi6o07jp4kTN0S

Lecture 01 - Introduction

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

Lecture 01 - Introduction, Subgradients

Lecture 02 - Subgradients (cont.)

Lecture 03 - Convergence Proof, Subgradient Methods, Linear Equality Constraints

Lecture 04 - Subgradient Method for Constrained Optimization, Convergence

Lecture 05 - Stochastic Programming, Localization and Cutting-Plane Methods

Lecture 06 - Analytic Center Cutting-Plane Method, Infeasible Start Newton Method Algorithm

Lecture 07 - ACCPM With Constraint Dropping, Ellipsoid Method

Lecture 08 - Recap: Ellipsoid Method, Primal Decomposition, Dual Decomposition

Lecture 09 - Recap: Primal Decomposition, Dual Decomposition

Lecture 10 - Decomposition Applications

Lecture 11 - Sequential Convex Programming

Lecture 12 - Recap: 'Difference Of Convex' Programming, Conjugate Gradient Method, Krylov Subspace

Lecture 13 - Recap: Conjugate Gradient Method and Krylov Subspace, Truncated Newton Method

Lecture 14 - Truncated Newton Method, L1-Norm Methods

Lecture 15 - L1-Norm Methods

Lecture 16 - Model Predictive Control

Lecture 17 - Stochastic Model Predictive Control, Branch and Bound Methods

Lecture 18 - Branch and Bound Methods