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

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 z...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 154; no. 1; pp. 217 - 234
Main Authors: Brito, Arnaldo S., da Cruz Neto, J. X., Lopes, Jurandir O., Oliveira, P. Roberto
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2012
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Convergence
Convex analysis
Engineering
Euclidean space
Inequalities
Mathematical functions
Mathematics
Mathematics and Statistics
Minimization
Operations Research/Decision Theory
Optimization
Programming
Regularization
Theory of Computation
Quasiconvex function
Quasiconvex linearly constrained problems
Proximal algorithm
Quasimonotone operator
Variational inequalities
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0002-0