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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Bibliographic Details
Published in:Vietnam journal of mathematics Vol. 46; no. 1; pp. 53 - 71
Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert, Nimana, Nimit
Format: Journal Article
Language:English
Published: Singapore Springer Singapore 01.03.2018
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2305-221X
2305-2228
2305-2228
DOI:10.1007/s10013-017-0256-9