Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1045.49018
Xu, H.K.; Kim, T.H.
Convergence of hybrid steepest-descent methods for variational inequalities. (English)
[J] J. Optimization Theory Appl. 119, No. 1, 185-201 (2003). ISSN 0022-3239; ISSN 1573-2878/e

Summary: Assume that $F$ is a nonlinear operator on a real Hilbert space $H$ which is $\eta$-strongly monotone and $\kappa$-Lipschitzian on a nonempty closed convex subset $C$ of $H$. Assume also that $C$ is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on $H$. We devise an iterative algorithm which generates a sequence ($x_n$) from an arbitrary initial point $x_0 \in H$. The sequence ($x_n$) is shown to converge in norm to the unique solution $u^{\ast}$ of the variational inequality $$\langle F(u^{\ast}), v - u^{\ast}\rangle \ge 0,\qquad \text{for } v \in C.$$ Applications to constrained pseudoinverses are included.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
90C30 Nonlinear programming

Keywords: iterative algorithms; hybrid steepest-descent methods; convergence; nonexpansive mappings; Hilbert space; constrained pseudoinverses

Cited in: Zbl 1158.65047 Zbl 1092.49013

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]