Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

Arnaldo S. Brito (), J. X. Cruz Neto (), Jurandir O. Lopes () and P. Roberto Oliveira ()
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Arnaldo S. Brito: Federal University of Rio de Janeiro
J. X. Cruz Neto: Federal University of Piaui
Jurandir O. Lopes: Federal University of Piaui
P. Roberto Oliveira: COPPE/Sistemas-Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 14, 217-234

Abstract: 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.

Keywords: Quasiconvex function; Proximal algorithm; Quasiconvex linearly constrained problems; Variational inequalities; Quasimonotone operator (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-012-0002-0

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