# Obviously Awesome

## Convex Optimization - book notes

### This post is in progress. It will be fleshed out as time permits.

• Convex Optimization (Boyd, Vandenberghe)

• Contents
• Preface

• Intro

Math optimization; Linear programming / least squares; Convex optimization; Non-linear optimization; Book outline; Notation

• Convex Sets

Affine & convex sets; examples; operations that preserve convexity; inequalities; separating & supporting hyperplanes; dual cones

• Convex Functions

Basic properties; operations that preserve convexity; conjugate functions; quasi-convex functions; log-concave & log-convex functions; convexity & generalized inequalities

• Convex Optimization

Intro; convex optimization; linear optimization; quadratic optimization; geometric programming; generalized inequality constraints; vector optimization

• Duality

Lagrange dual function; Lagrange dual problem; geometric interpretation; saddle-point interpretation; optimality conditions; pertubation & sensitivity analysis; examples; theorems of alternatives; generalized inequalities

• Approximation & fitting

Norm approximation; least-norm problems; regularized approximation; robust approximation; function fitting & interpolation

• Statistical estimation

Parametric distributions; non-parametric distributions; optimal detector design & hypothesis testing; Chebyshev & Chernoff bounds; experiment design

• Geometric problems

Projection on a set; distances between sets; Euclidean distances & angle problems; extremal volume ellipsoids; centering; classification; placement & location; floorplanning

• Unconstrained optimization

Problems; descent methods; gradient descent; steepest descent; Newton’s method; self-concordance; implementation

• Equality-constrained minimization

Problems; Newton’s method; infeasible-start Newton’s method; implementation

• Interior-point methods

Problems; log-barrier function & central path; barrier method; feasibility & phase I methods; complexity analysis; general-inequality problems; primal-dual methods; implementation

• Appendix: Math

Norms; analysis; functions; derivatives; linear algebra