The primal-dual active set strategy as a semismooth Newton method. (English) Zbl 1080.90074

Hintermüller, M.; Ito, K.; Kunisch, K.

SIAM J. Optim. 13, No. 3, 865-888 (2003).

The authors present complementarity problems in terms of constrained optimal control problems. In fact it is shown that the prime-dual active set method can be interpreted as a semi-smooth Newton method. This opens up a new interpretation and perspective of analyzing the the prime-dual active set method. The authors have presented a large body of material which deserves to be better known. The exposition is uniformly clear.

Reviewer: Akrur Behera (Rourkela)

MSC:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K10	Numerical optimization and variational techniques
90C53	Methods of quasi-Newton type

Keywords:

complementarity problems; function spaces; semismooth Newton method