Partially relaxed cocoercive variational inequalities and auxiliary problem principle

Ram U. Verma

International Journal of Stochastic Analysis, 2004, vol. 2004, 1-6

Abstract:

Let T : K → H be a mapping from a nonempty closed convex subset K of a finite-dimensional Hilbert space H into H . Let f : K → ℝ be proper, convex, and lower semicontinuous on K and let h : K → ℝ be continuously Frećhet-differentiable on K with h ′ (gradient of h ), α -strongly monotone, and β -Lipschitz continuous on K . Then the sequence { x k } generated by the general auxiliary problem principle converges to a solution x * of the variational inequality problem (VIP) described as follows: find an element x * ∈ K such that 〈 T ( x * ) , x − x * 〉 + f ( x ) − f ( x * ) ≥ 0 for all x ∈ K .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:786703

DOI: 10.1155/S1048953304305010

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