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Homotopy Methods for Solving Variational Inequalities in Unbounded Sets

Author

Listed:
  • Qing Xu
  • Bo Yu
  • Guo-Chen Feng

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

Suggested Citation

  • Qing Xu & Bo Yu & Guo-Chen Feng, 2005. "Homotopy Methods for Solving Variational Inequalities in Unbounded Sets," Journal of Global Optimization, Springer, vol. 31(1), pages 121-131, January.
    • Handle: RePEc:spr:jglopt:v:31:y:2005:i:1:p:121-131
    DOI: 10.1007/s10898-004-4272-4
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    Cited by:

    1. Yang Zhan & Peixuan Li & Chuangyin Dang, 2020. "A differentiable path-following algorithm for computing perfect stationary points," Computational Optimization and Applications, Springer, vol. 76(2), pages 571-588, June.
    2. Zhengyong Zhou & Bo Yu, 2014. "A smoothing homotopy method for variational inequality problems on polyhedral convex sets," Journal of Global Optimization, Springer, vol. 58(1), pages 151-168, January.

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