An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems

We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under s...

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Vydané v:Vietnam journal of mathematics Ročník 46; číslo 1; s. 53 - 71
Hlavní autori: Boţ, Radu Ioan, Csetnek, Ernö Robert, Nimana, Nimit
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Singapore Springer Singapore 01.03.2018
Springer Nature B.V
Predmet:
Computational geometry
Convergence
Convexity
Mathematical programming
Mathematics
Mathematics and Statistics
Optimization
65K05
Penalization
90C25
Fenchel conjugate
47H05
Proximal-gradient algorithm
Inertial algorithm
ISSN:2305-221X, 2305-2228, 2305-2228
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Abstract We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.
AbstractList We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.
We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.
Author Boţ, Radu Ioan
Csetnek, Ernö Robert
Nimana, Nimit
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  givenname: Ernö Robert
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  givenname: Nimit
  surname: Nimana
  fullname: Nimana, Nimit
  organization: Department of Mathematics, Faculty of Science, Naresuan University
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Issue 1
Keywords 65K05
Penalization
90C25
Fenchel conjugate
47H05
Proximal-gradient algorithm
Inertial algorithm
Language English
License The Author(s) 2017.
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Snippet We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower...
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SubjectTerms Computational geometry
Convergence
Convexity
Mathematical programming
Mathematics
Mathematics and Statistics
Optimization
Title An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems
URI https://link.springer.com/article/10.1007/s10013-017-0256-9
https://www.ncbi.nlm.nih.gov/pubmed/32714952
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https://pubmed.ncbi.nlm.nih.gov/PMC7370989
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