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An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems
- Source :
- Vietnam Journal of Mathematics
- Publication Year :
- 2017
-
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.
- Subjects :
- Convex analysis
Mathematical optimization
021103 operations research
47H05
General Mathematics
Proximal-gradient algorithm
010102 general mathematics
0211 other engineering and technologies
Proper convex function
65K05
02 engineering and technology
Subderivative
01 natural sciences
Bilevel optimization
Article
90C25
Inertial algorithm
Fenchel conjugate
Convex optimization
Proximal gradient methods for learning
Differentiable function
0101 mathematics
Convex conjugate
Penalization
Mathematics
Subjects
Details
- ISSN :
- 23052228
- Volume :
- 46
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Vietnam journal of mathematics
- Accession number :
- edsair.doi.dedup.....474fbb5774bfc4f3f4cf500317f3aa27