Hemiequilibrium problems. (English) Zbl 1069.49011

Noor, Muhammad Aslam

J. Appl. Math. Stochastic Anal. 2004, No. 3, 235-244 (2004).

The author considers an extension of the hemivariational inequality in Hilbert spaces, where the variational inequality term is replaced by a nonlinear bi-function. Extensions of the Minty lemma and some iterative methods based on the auxiliary problem principle are presented. Unfortunately, the paper contains many typos and ambiguities which may cause misunderstanding of the results.

Reviewer: Igor V. Konnov (Kazan)

MSC:

49J40	Variational inequalities
47J20	Variational and other types of inequalities involving nonlinear operators (general)
49J52	Nonsmooth analysis
65K10	Numerical optimization and variational techniques

Keywords:

hemiequilibrium problems; Hilbert spaces; auxiliary problem principle