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1	Projection Methods for Variational Inequalities Governed by Inverse Strongly Monotone Operators Lin, Yen-Ru 26 June 2010 (has links) Consider the variational inequality (VI) x* ∈C, ‹Fx, x - x ›≥0, x∈C () where C is a nonempty closed convex subset of a real Hilbert space H and F : C¡÷ H is a monotone operator form C into H. It is known that if F is strongly monotone and Lipschitzian, then VI () is equivalently turned into a fixed point problem of a contraction; hence Banach's contraction principle applies. However, in the case where F is inverse strongly monotone, VI () is equivalently transformed into a fixed point problem of a nonexpansive mapping. The purpose of this paper is to present some results which apply iterative methods for nonexpansive mappings to solve VI (). We introduce Mann's algorithm and Halpern's algorithm and prove that the sequences generated by these algorithms converge weakly and respectively, strongly to a solution of VI (*), under appropriate conditions imposed on the parameter sequences in the algorithms. fixed point Variational inequality Mann's algorithm projection monotone mapping demiclosedness principle Halpern's algorithm nonexpansive mapping inverse strongly monotone strongly monotone weak convergence strongly convergence