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A Subgradient-Like Algorithm for Solving Vector Convex Inequalities

Author

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  • J. Y. Bello Cruz

    (Universidade Federal de Goiás)

  • L. R. Lucambio Pérez

    (Universidade Federal de Goiás, Campus Samambaia)

Abstract

In this paper, we propose a strongly convergent variant of Robinson’s subgradient algorithm for solving a system of vector convex inequalities in Hilbert spaces. The advantage of the proposed method is that it converges strongly, when the problem has solutions, under mild assumptions. The proposed algorithm also has the following desirable property: the sequence converges to the solution of the problem, which lies closest to the starting point and remains entirely in the intersection of three balls with radius less than the initial distance to the solution set.

Suggested Citation

  • J. Y. Bello Cruz & L. R. Lucambio Pérez, 2014. "A Subgradient-Like Algorithm for Solving Vector Convex Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 392-404, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0300-1
    DOI: 10.1007/s10957-013-0300-1
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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.
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    Cited by:

    1. Alfredo N. Iusem & Jefferson G. Melo & Ray G. Serra, 2021. "A Strongly Convergent Proximal Point Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 183-200, July.

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