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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Veröffentlicht in:Journal of optimization theory and applications Jg. 154; H. 1; S. 217 - 234
Hauptverfasser: Brito, Arnaldo S., da Cruz Neto, J. X., Lopes, Jurandir O., Oliveira, P. Roberto
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.07.2012
Springer Nature B.V
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ISSN:0022-3239, 1573-2878
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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.
AbstractList 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.
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.[PUBLICATION ABSTRACT]
Author Brito, Arnaldo S.
da Cruz Neto, J. X.
Oliveira, P. Roberto
Lopes, Jurandir O.
Author_xml – sequence: 1
  givenname: Arnaldo S.
  surname: Brito
  fullname: Brito, Arnaldo S.
  organization: Federal University of Rio de Janeiro
– sequence: 2
  givenname: J. X.
  surname: da Cruz Neto
  fullname: da Cruz Neto, J. X.
  organization: Federal University of Piaui
– sequence: 3
  givenname: Jurandir O.
  surname: Lopes
  fullname: Lopes, Jurandir O.
  email: jurandir@ufpi.br
  organization: Federal University of Piaui
– sequence: 4
  givenname: P. Roberto
  surname: Oliveira
  fullname: Oliveira, P. Roberto
  organization: COPPE/Sistemas-Universidade Federal do Rio de Janeiro
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Keywords Quasiconvex function
Quasiconvex linearly constrained problems
Proximal algorithm
Quasimonotone operator
Variational inequalities
Language English
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Snippet In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general...
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StartPage 217
SubjectTerms 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
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Title Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints
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