Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems

We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective is the sum of a strongly quasiconvex function plus the standard quadratic regularization term for optimization problems. We prove, under sui...

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Vydané v:Journal of optimization theory and applications Ročník 193; číslo 1-3; s. 443 - 461
Hlavní autori: Iusem, A., Lara, F.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.06.2022
Springer Nature B.V
Predmet:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Convexity
Engineering
Equilibrium
Equilibrium methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Regularization
Theory of Computation
Quasiconvexity
Strong quasiconvexity
Pseudomonotonicity
Proximal point algorithms
Equilibrium problems
ISSN:0022-3239, 1573-2878
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Abstract We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective is the sum of a strongly quasiconvex function plus the standard quadratic regularization term for optimization problems. We prove, under suitable additional assumptions, convergence of the generated sequence to a solution of the equilibrium problem, whenever the bifunction is strongly quasiconvex in its second argument, thus extending the validity of the convergence analysis of proximal point methods for equilibrium problems beyond the standard assumption of convexity of the bifunction in the second argument.
AbstractList We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective is the sum of a strongly quasiconvex function plus the standard quadratic regularization term for optimization problems. We prove, under suitable additional assumptions, convergence of the generated sequence to a solution of the equilibrium problem, whenever the bifunction is strongly quasiconvex in its second argument, thus extending the validity of the convergence analysis of proximal point methods for equilibrium problems beyond the standard assumption of convexity of the bifunction in the second argument.
Author Lara, F.
Iusem, A.
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  surname: Lara
  fullname: Lara, F.
  organization: Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá
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Issue 1-3
Keywords Quasiconvexity
Strong quasiconvexity
Pseudomonotonicity
Proximal point algorithms
Equilibrium problems
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Snippet We propose a proximal point method for quasiconvex pseudomonotone equilibrium problems. The subproblems of the method are optimization problems whose objective...
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SubjectTerms Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Convexity
Engineering
Equilibrium
Equilibrium methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Regularization
Theory of Computation
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Title Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems
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