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Full convergence of an approximate projection method for nonsmooth variational inequalities

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  • Bello Cruz, J.Y.
  • Iusem, A.N.

Abstract

We analyze an explicit method for solving nonsmooth variational inequality problems, establishing convergence of the whole sequence, under paramonotonicity of the operator. Previous results on similar methods required much more demanding assumptions, like coerciveness of the operator.

Suggested Citation

  • Bello Cruz, J.Y. & Iusem, A.N., 2015. "Full convergence of an approximate projection method for nonsmooth variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 2-13.
    • Handle: RePEc:eee:matcom:v:114:y:2015:i:c:p:2-13
    DOI: 10.1016/j.matcom.2010.05.026
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    References listed on IDEAS

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    1. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    2. Masao Fukushima, 1983. "An Outer Approximation Algorithm for Solving General Convex Programs," Operations Research, INFORMS, vol. 31(1), pages 101-113, February.
    3. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, June.
    4. Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
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    Cited by:

    1. Alfredo N. Iusem & Alejandro Jofré & Philip Thompson, 2019. "Incremental Constraint Projection Methods for Monotone Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 236-263, February.
    2. J. Y. Bello Cruz & R. Díaz Millán, 2016. "A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces," Journal of Global Optimization, Springer, vol. 65(3), pages 597-614, July.

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