Trilevel and multilevel optimization using monotone operator theory
Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shafiei, Allahkaram [verfasserIn] Kungurtsev, Vyacheslav [verfasserIn] Marecek, Jakub [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematical methods of operations research - Springer Berlin Heidelberg, 1956, 99(2024), 1-2 vom: 28. Feb., Seite 77-114 |
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| Übergeordnetes Werk: |
volume:99 ; year:2024 ; number:1-2 ; day:28 ; month:02 ; pages:77-114 |
| Links: |
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| DOI / URN: |
10.1007/s00186-024-00852-5 |
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| Katalog-ID: |
SPR055726410 |
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| 520 | |a Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. | ||
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| 650 | 4 | |a Tri-level optimization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multi-level minimization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Non-expansive mappings |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kungurtsev, Vyacheslav |e verfasserin |0 (orcid)0000-0003-2229-8824 |4 aut | |
| 700 | 1 | |a Marecek, Jakub |e verfasserin |0 (orcid)0000-0003-0839-0691 |4 aut | |
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10.1007/s00186-024-00852-5 doi (DE-627)SPR055726410 (SPR)s00186-024-00852-5-e DE-627 ger DE-627 rakwb eng 330 510 VZ 330 510 VZ 85.03 bkl Shafiei, Allahkaram verfasserin (orcid)0000-0002-1415-2166 aut Trilevel and multilevel optimization using monotone operator theory 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. Variational inequality (dpeaa)DE-He213 Bi-level optimization (dpeaa)DE-He213 Tri-level optimization (dpeaa)DE-He213 Multi-level minimization (dpeaa)DE-He213 Non-expansive mappings (dpeaa)DE-He213 Kungurtsev, Vyacheslav verfasserin (orcid)0000-0003-2229-8824 aut Marecek, Jakub verfasserin (orcid)0000-0003-0839-0691 aut Enthalten in Mathematical methods of operations research Springer Berlin Heidelberg, 1956 99(2024), 1-2 vom: 28. Feb., Seite 77-114 (DE-627)253770734 (DE-600)1459420-1 1432-5217 nnns volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 https://dx.doi.org/10.1007/s00186-024-00852-5 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 VZ AR 99 2024 1-2 28 02 77-114 |
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10.1007/s00186-024-00852-5 doi (DE-627)SPR055726410 (SPR)s00186-024-00852-5-e DE-627 ger DE-627 rakwb eng 330 510 VZ 330 510 VZ 85.03 bkl Shafiei, Allahkaram verfasserin (orcid)0000-0002-1415-2166 aut Trilevel and multilevel optimization using monotone operator theory 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. Variational inequality (dpeaa)DE-He213 Bi-level optimization (dpeaa)DE-He213 Tri-level optimization (dpeaa)DE-He213 Multi-level minimization (dpeaa)DE-He213 Non-expansive mappings (dpeaa)DE-He213 Kungurtsev, Vyacheslav verfasserin (orcid)0000-0003-2229-8824 aut Marecek, Jakub verfasserin (orcid)0000-0003-0839-0691 aut Enthalten in Mathematical methods of operations research Springer Berlin Heidelberg, 1956 99(2024), 1-2 vom: 28. Feb., Seite 77-114 (DE-627)253770734 (DE-600)1459420-1 1432-5217 nnns volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 https://dx.doi.org/10.1007/s00186-024-00852-5 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 VZ AR 99 2024 1-2 28 02 77-114 |
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10.1007/s00186-024-00852-5 doi (DE-627)SPR055726410 (SPR)s00186-024-00852-5-e DE-627 ger DE-627 rakwb eng 330 510 VZ 330 510 VZ 85.03 bkl Shafiei, Allahkaram verfasserin (orcid)0000-0002-1415-2166 aut Trilevel and multilevel optimization using monotone operator theory 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. Variational inequality (dpeaa)DE-He213 Bi-level optimization (dpeaa)DE-He213 Tri-level optimization (dpeaa)DE-He213 Multi-level minimization (dpeaa)DE-He213 Non-expansive mappings (dpeaa)DE-He213 Kungurtsev, Vyacheslav verfasserin (orcid)0000-0003-2229-8824 aut Marecek, Jakub verfasserin (orcid)0000-0003-0839-0691 aut Enthalten in Mathematical methods of operations research Springer Berlin Heidelberg, 1956 99(2024), 1-2 vom: 28. Feb., Seite 77-114 (DE-627)253770734 (DE-600)1459420-1 1432-5217 nnns volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 https://dx.doi.org/10.1007/s00186-024-00852-5 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 VZ AR 99 2024 1-2 28 02 77-114 |
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10.1007/s00186-024-00852-5 doi (DE-627)SPR055726410 (SPR)s00186-024-00852-5-e DE-627 ger DE-627 rakwb eng 330 510 VZ 330 510 VZ 85.03 bkl Shafiei, Allahkaram verfasserin (orcid)0000-0002-1415-2166 aut Trilevel and multilevel optimization using monotone operator theory 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. Variational inequality (dpeaa)DE-He213 Bi-level optimization (dpeaa)DE-He213 Tri-level optimization (dpeaa)DE-He213 Multi-level minimization (dpeaa)DE-He213 Non-expansive mappings (dpeaa)DE-He213 Kungurtsev, Vyacheslav verfasserin (orcid)0000-0003-2229-8824 aut Marecek, Jakub verfasserin (orcid)0000-0003-0839-0691 aut Enthalten in Mathematical methods of operations research Springer Berlin Heidelberg, 1956 99(2024), 1-2 vom: 28. Feb., Seite 77-114 (DE-627)253770734 (DE-600)1459420-1 1432-5217 nnns volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 https://dx.doi.org/10.1007/s00186-024-00852-5 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 VZ AR 99 2024 1-2 28 02 77-114 |
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Enthalten in Mathematical methods of operations research 99(2024), 1-2 vom: 28. Feb., Seite 77-114 volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 |
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Enthalten in Mathematical methods of operations research 99(2024), 1-2 vom: 28. Feb., Seite 77-114 volume:99 year:2024 number:1-2 day:28 month:02 pages:77-114 |
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Shafiei, Allahkaram @@aut@@ Kungurtsev, Vyacheslav @@aut@@ Marecek, Jakub @@aut@@ |
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Shafiei, Allahkaram |
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330 510 VZ 85.03 bkl Trilevel and multilevel optimization using monotone operator theory Variational inequality (dpeaa)DE-He213 Bi-level optimization (dpeaa)DE-He213 Tri-level optimization (dpeaa)DE-He213 Multi-level minimization (dpeaa)DE-He213 Non-expansive mappings (dpeaa)DE-He213 |
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ddc 330 bkl 85.03 misc Variational inequality misc Bi-level optimization misc Tri-level optimization misc Multi-level minimization misc Non-expansive mappings |
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trilevel and multilevel optimization using monotone operator theory |
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Trilevel and multilevel optimization using monotone operator theory |
| abstract |
Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. © The Author(s) 2024 |
| abstractGer |
Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. © The Author(s) 2024 |
| abstract_unstemmed |
Abstract We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters. © The Author(s) 2024 |
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Trilevel and multilevel optimization using monotone operator theory |
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https://dx.doi.org/10.1007/s00186-024-00852-5 |
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Kungurtsev, Vyacheslav Marecek, Jakub |
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Kungurtsev, Vyacheslav Marecek, Jakub |
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10.1007/s00186-024-00852-5 |
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2024-07-03T17:37:27.499Z |
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| score |
7.401552 |