[Preface]
Math optimization
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
Basic properties
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
Lagrange dual function
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
Parametric distributions
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
Problems
descent methods
gradient descent
steepest descent
Newton's method; self-concordance
implementation
Problems
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
Norms
analysis
functions
derivatives
linear algebra
Single-constraint optimization
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