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

[Contents]
[Preface]

Math optimization

Linear programming / least squares

Convex optimization; Non-linear optimization

Book outline

Notation

Linear programming / least squares

Convex optimization; Non-linear optimization

Book outline

Notation

Affine & convex sets

examples

operations that preserve convexity

inequalities

separating & supporting hyperplanes

dual cones

examples

operations that preserve convexity

inequalities

separating & supporting hyperplanes

dual cones

Basic properties

operations that preserve convexity

conjugate functions; quasi-convex functions

log-concave & log-convex functions

convexity & generalized inequalities

operations that preserve convexity

conjugate functions; quasi-convex functions

log-concave & log-convex functions

convexity & generalized inequalities

Intro

convex optimization

linear optimization

quadratic optimization; geometric programming

generalized inequality constraints

vector optimization

convex optimization

linear optimization

quadratic optimization; geometric programming

generalized inequality constraints

vector optimization

Lagrange dual function

Lagrange dual problem

geometric interpretation; saddle-point interpretation

optimality conditions

pertubation & sensitivity analysis

examples

theorems of alternatives

generalized inequalities

Lagrange dual problem

geometric interpretation; saddle-point interpretation

optimality conditions

pertubation & sensitivity analysis

examples

theorems of alternatives

generalized inequalities

Norm approximation

least-norm problems

regularized approximation

robust approximation

function fitting & interpolation

least-norm problems

regularized approximation

robust approximation

function fitting & interpolation

Parametric distributions

non-parametric distributions

optimal detector design & hypothesis testing

Chebyshev & Chernoff bounds

experiment design

non-parametric distributions

optimal detector design & hypothesis testing

Chebyshev & Chernoff bounds

experiment design

Projection on a set

distances between sets

Euclidean distances & angle problems

extremal volume ellipsoids

centering

classification

placement & location

floorplanning

distances between sets

Euclidean distances & angle problems

extremal volume ellipsoids

centering

classification

placement & location

floorplanning

Problems

descent methods

gradient descent

steepest descent

Newton's method; self-concordance

implementation

descent methods

gradient descent

steepest descent

Newton's method; self-concordance

implementation

Problems

Newton's method

infeasible-start Newton's method

implementation

Newton's method

infeasible-start Newton's method

implementation

Problems

log-barrier function & central path

barrier method

feasibility & phase I methods

complexity analysis

general-inequality problems

primal-dual methods

implementation

log-barrier function & central path

barrier method

feasibility & phase I methods

complexity analysis

general-inequality problems

primal-dual methods

implementation

Norms

analysis

functions

derivatives

linear algebra

analysis

functions

derivatives

linear algebra

Single-constraint optimization

S-procedure

symmetric matrix values

strong duality proofs

S-procedure

symmetric matrix values

strong duality proofs

Matrix structures & algorithm complexity

solving linear equations with factored matrices

LU, Cholesky & LDL factorization

block elimination & Schur complements

solving under-determined linear equations

solving linear equations with factored matrices

LU, Cholesky & LDL factorization

block elimination & Schur complements

solving under-determined linear equations