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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Vydáno v:Journal of optimization theory and applications Ročník 154; číslo 1; s. 217 - 234
Hlavní autoři: Brito, Arnaldo S., da Cruz Neto, J. X., Lopes, Jurandir O., Oliveira, P. Roberto
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.07.2012
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0002-0