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

被引：12
作者：
Boţ R.I. [1 ]
Csetnek E.R. [1 ]
Nimana N. [2 ]
机构：
[1] Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna
[2] Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok
来源：
Vietnam Journal of Mathematics | 2018年 / 46卷 / 1期
基金：
奥地利科学基金会;
关键词：
Fenchel conjugate; Inertial algorithm; Penalization; Proximal-gradient algorithm;
D O I：
10.1007/s10013-017-0256-9
中图分类号：
学科分类号：
摘要：
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. © 2017, The Author(s).
引用
收藏
页码：53 / 71
页数：18
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