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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| Veröffentlicht in: | Vietnam journal of mathematics Jg. 46; H. 1; S. 53 - 71 |
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01.03.2018
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Radu Ioan surname: Boţ fullname: Boţ, Radu Ioan email: radu.bot@univie.ac.at organization: Faculty of Mathematics, University of Vienna – sequence: 2 givenname: Ernö Robert surname: Csetnek fullname: Csetnek, Ernö Robert organization: Faculty of Mathematics, University of Vienna – sequence: 3 givenname: Nimit surname: Nimana fullname: Nimana, Nimit organization: Department of Mathematics, Faculty of Science, Naresuan University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/32714952$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1137/130942954 10.1137/110820300 10.1080/02331934.2016.1181759 10.1007/s10957-013-0296-6 10.1137/080716542 10.1016/j.jde.2016.11.009 10.1007/s11075-015-0007-5 10.1007/s10957-015-0730-z 10.1016/j.jmaa.2015.11.032 10.1007/s11228-014-0274-7 10.1080/00036811.2016.1157589 10.1016/S0377-0427(02)00906-8 10.1137/060655183 10.1080/01630563.2015.1042113 10.1137/15M1046095 10.1017/CBO9781139087322 10.1137/140980910 10.1137/S0363012998335802 10.1007/s11228-010-0140-1 10.1016/j.cam.2007.07.021 10.1023/A:1011253113155 10.1007/978-1-4419-9467-7 10.1007/s13675-015-0045-8 10.1016/j.jde.2009.06.014 10.1007/s10957-014-0700-x 10.1137/100789464 10.1007/s10957-011-9936-x 10.1007/s10013-013-0050-2 10.1137/130910294 10.1137/15100463X 10.1137/S1052623403427859 10.1142/5021 10.1007/s11228-017-0409-8 10.1007/978-3-642-04900-2 10.1007/s11590-017-1158-1 10.1090/tran/6965 |
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| Keywords | 65K05 Penalization 90C25 Fenchel conjugate 47H05 Proximal-gradient algorithm Inertial algorithm |
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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 |
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