Convex Optimization (Boyd, Vandenberghe)
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
Equality-constrained minimization
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
Appendix: Two-quadratic-function problems
Single-constraint optimization; S-procedure; symmetric matrix values; strong duality proofs
Appendix: Numerical linear algebra
Matrix structures & algorithm complexity; solving linear equations with factored matrices; LU, Cholesky & LDL factorization; block elimination & Schur complements; solving under-determined linear equations