Abstract
In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones.
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Acknowledgements
A.S. Brito was supported in part by CAPES. J.X.C. Neto was supported in part by CNPq Grant 301625/2008-5. J.O. Lopes was supported in part by INCTMAT/CNPq. P.R. Oliveira was supported in part by CNPq.
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Communicated by Alfredo N. Iusem.
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Brito, A.S., da Cruz Neto, J.X., Lopes, J.O. et al. Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints. J Optim Theory Appl 154, 217–234 (2012). https://doi.org/10.1007/s10957-012-0002-0
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DOI: https://doi.org/10.1007/s10957-012-0002-0