Homotopy Methods for Solving Variational Inequalities in Unbounded Sets

Qing Xu (), Bo Yu () and Guo-Chen Feng ()

Journal of Global Optimization, 2005, vol. 31, issue 1, 131 pages

Abstract: In this paper, for solving the finite-dimensional variational inequality problem $$(x-x*)^{T} F(x*)\geq 0, \quad \forall x\in X,$$ where F is a $$C^r (r gt; 1)$$ mapping from X to R n , X= $$ { x \in R^{n} : g(x) leq; 0}$$ is nonempty (not necessarily bounded) and $${\it g}({\it x}): R^{n} \rightarrow R^{m}$$ is a convex C r+1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial point in X to a solution of the variational inequality problem is proven. It leads to an implementable and globally convergent algorithm and gives a new and constructive proof of existence of solution. Copyright Springer Science+Business Media New York 2005

Keywords: Homotopy method; Interior point method; Variational inequality (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-004-4272-4

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