 
Summary: 5. Constrained nonlinear optimization
Version: 20112010
Material (partially)
Chapter 12 in [FKS] (pp.283320)
A reference e.g. L.12.2 refers to the corresponding Lemma
in the book [FKS]
CO, Chapter 5 p 1
5.1 Introduction
We consider the minimization problem
(P) min f(x) s.t. x F
where the feasible set is given by
F = {x Rn
 gj(x) 0, j J}
with J = {1, . . . , m}, f, gj C1(Rn, R)
Rem. We skip additional equality constraints hi(x) = 0 to
avoid technical difficulties.
Recall for x F the active index set Jx :
Jx = {j J  gj(x) = 0}
CO, Chapter 5 p 2
5.2 Optimality conditions
