New mixed integer fractional programming problem and some multi-objective models for sparse optimization
We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of...
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| Vydáno v: | Soft computing (Berlin, Germany) Ročník 27; číslo 21; s. 15893 - 15904 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.11.2023
Springer Nature B.V |
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| ISSN: | 1432-7643, 1433-7479 |
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| Abstract | We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of the problem, which comes out in the form of a fractional programming problem (FPP). In particular, we consider a possible way for tackling FPP by reformulating it via a DC (Difference of Convex) decomposition. We also overview the SVM models and the related Feature Selection in terms of multi-objective optimization. The results of some numerical experiments on benchmark classification datasets are reported. |
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| AbstractList | We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of the problem, which comes out in the form of a fractional programming problem (FPP). In particular, we consider a possible way for tackling FPP by reformulating it via a DC (Difference of Convex) decomposition. We also overview the SVM models and the related Feature Selection in terms of multi-objective optimization. The results of some numerical experiments on benchmark classification datasets are reported. |
| Author | Gaudioso, Manlio Pirouz, Behzad |
| Author_xml | – sequence: 1 givenname: Behzad orcidid: 0000-0003-4156-4454 surname: Pirouz fullname: Pirouz, Behzad organization: Dipartimento di Ingegneria Informatica Modellistica, Elettronica e Sistemistica, Universitá della Calabria – sequence: 2 givenname: Manlio surname: Gaudioso fullname: Gaudioso, Manlio email: gaudioso@dimes.unical.it organization: Dipartimento di Ingegneria Informatica Modellistica, Elettronica e Sistemistica, Universitá della Calabria, ICAR-CNR |
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| Cites_doi | 10.11648/j.acm.20150402.13 10.1007/s10589-008-9202-9 10.1016/j.cor.2017.06.001 10.1007/978-1-4419-9467-7 10.1177/105971239400300102 10.1137/110827144 10.1007/s11590-019-01482-1 10.3390/ijgi10060424 10.1007/BF02139472 10.1109/TPAMI.1981.4767177 10.1137/S1052623496307510 10.1038/323533a0 10.1007/s10107-017-1181-0 10.1080/10556780600628212 10.1016/j.swevo.2012.09.003 10.1017/CBO9780511801389 10.1080/02331934.2011.587006 10.1109/TSP.2009.2026004 10.1016/j.ejor.2018.06.012 10.2298/FIL1907149D 10.1137/100808563 10.1016/j.patrec.2009.10.013 10.1016/j.ejor.2020.08.045 10.1287/moor.2017.0873 10.1007/BF02564711 10.1214/15-AOS1388 10.1007/s10107-015-0894-1 10.1137/16M1059333 10.1016/j.apm.2015.03.022 10.1007/s10898-017-0568-z 10.1109/CDC.2014.7040063 10.1016/B978-1-55860-335-6.50023-4 10.1109/CEC.2012.6256452 10.1137/21M1391481 10.1007/978-3-540-71618-1_27 10.1007/978-3-642-99789-1_13 10.1145/1569901.1570040 |
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| Keywords | Sparse optimization Fractional programming Multi-objective machine learning Mixed integer problem norm |
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| References | Chen, Miao, Wang (CR8) 2010; 31 Cristianini, Shawe-Taylor (CR9) 2000 Pilanci, Wainwright, El Ghaoui (CR38) 2015; 151 Gambella, Ghaddar, Naoum-Sawaya (CR16) 2021; 290 Ceyhan, Köksalan, Lokman (CR7) 2019; 272 Ehrgott (CR13) 2005 Nolfi, Parisi, Elman (CR35) 1994; 3 Pintér, Linder, Chin (CR39) 2006; 21 Jafari-Petroudi, Pirouz (CR30) 2015; 4 Petroudi, Pirouz, Akbiyik (CR37) 2022; 10 CR34 CR33 CR32 Wright (CR52) 2012; 22 CR31 Ferrante, Pirouz, Pirouz (CR42) 2021; 10 Bach, Jenatton, Mairal (CR2) 2011; 5 Jafari-Petroudi, Pirouz (CR28) 2016; 3 Rinaldi, Schoen, Sciandrone (CR44) 2010; 46 CR6 CR5 CR43 CR41 Rumelhart, Hinton, Williams (CR46) 1986; 323 Bauschke, Combettes (CR3) 2011 Dutta, Kaya (CR12) 2011; 60 Soubies, Blanc-Féraud, Aubert (CR48) 2017; 27 Gasso, Rakotomamonjy, Canu (CR17) 2009; 57 Das, Dennis (CR10) 1998; 8 Bertsimas, King, Mazumder (CR4) 2016; 44 Gaudioso, Gorgone, Hiriart-Urruty (CR22) 2020; 14 Al-Ani, Alsukker, Khushaba (CR1) 2013; 9 Dolatnezhadsomarin, Khorram, Pourkarimi (CR11) 2019; 33 CR18 Gaudioso, Gorgone, Labbé (CR19) 2017; 87 Wu, Ding, Sun (CR53) 2014; 24 Rodenas, Lopez, Verastegui (CR45) 1999; 7 CR14 Jy, Takeda, Tono (CR24) 2018; 169 CR51 Swain, Davis (CR49) 1981; 3 Sivri, Albayrak, Temelcan (CR47) 2018; 181 Petroudi, Pirouz (CR36) 2015; 3 Gaudioso, Giallombardo, Miglionico (CR21) 2018; 71 Pirouz, Khorram (CR40) 2016; 49 CR29 Ghane-Kanafi, Khorram (CR23) 2015; 39 Haykin, Network (CR26) 2004; 2 CR27 CR25 Watson (CR50) 1992; 2 Forman (CR15) 2003; 3 Gaudioso, Giallombardo, Miglionico (CR20) 2018; 43 E Soubies (8839_CR48) 2017; 27 JD Pintér (8839_CR39) 2006; 21 G Forman (8839_CR15) 2003; 3 SHJ Petroudi (8839_CR37) 2022; 10 A Al-Ani (8839_CR1) 2013; 9 8839_CR29 S Jafari-Petroudi (8839_CR28) 2016; 3 8839_CR27 S Nolfi (8839_CR35) 1994; 3 8839_CR25 G Jy (8839_CR24) 2018; 169 D Bertsimas (8839_CR4) 2016; 44 N Cristianini (8839_CR9) 2000 M Ehrgott (8839_CR13) 2005 8839_CR51 SHJ Petroudi (8839_CR36) 2015; 3 8839_CR5 M Gaudioso (8839_CR20) 2018; 43 S Haykin (8839_CR26) 2004; 2 8839_CR18 8839_CR6 DE Rumelhart (8839_CR46) 1986; 323 8839_CR14 A Ghane-Kanafi (8839_CR23) 2015; 39 M Gaudioso (8839_CR21) 2018; 71 F Rinaldi (8839_CR44) 2010; 46 C Gambella (8839_CR16) 2021; 290 RG Rodenas (8839_CR45) 1999; 7 8839_CR43 8839_CR41 Y Chen (8839_CR8) 2010; 31 SJ Wright (8839_CR52) 2012; 22 I Das (8839_CR10) 1998; 8 M Pilanci (8839_CR38) 2015; 151 PH Swain (8839_CR49) 1981; 3 AP Ferrante (8839_CR42) 2021; 10 A Dolatnezhadsomarin (8839_CR11) 2019; 33 J Dutta (8839_CR12) 2011; 60 B Pirouz (8839_CR40) 2016; 49 M Sivri (8839_CR47) 2018; 181 H Bauschke (8839_CR3) 2011 M Gaudioso (8839_CR19) 2017; 87 G Gasso (8839_CR17) 2009; 57 8839_CR31 8839_CR32 F Bach (8839_CR2) 2011; 5 SH Jafari-Petroudi (8839_CR30) 2015; 4 B Wu (8839_CR53) 2014; 24 M Gaudioso (8839_CR22) 2020; 14 8839_CR33 G Ceyhan (8839_CR7) 2019; 272 8839_CR34 GA Watson (8839_CR50) 1992; 2 |
| References_xml | – volume: 4 start-page: 47 year: 2015 end-page: 52 ident: CR30 article-title: A particular matrix, its inversion and some norms publication-title: Appl Comput Math doi: 10.11648/j.acm.20150402.13 – volume: 46 start-page: 467 issue: 3 year: 2010 end-page: 486 ident: CR44 article-title: Concave programming for minimizing the zero-norm over polyhedral sets publication-title: Comput Optim Appl doi: 10.1007/s10589-008-9202-9 – volume: 87 start-page: 137 year: 2017 end-page: 145 ident: CR19 article-title: Lagrangian relaxation for SVM feature selection publication-title: Comput Oper Res doi: 10.1016/j.cor.2017.06.001 – ident: CR51 – year: 2011 ident: CR3 publication-title: Convex analysis and monotone operator theory in Hilbert spaces doi: 10.1007/978-1-4419-9467-7 – volume: 3 start-page: 82 issue: 4 year: 2016 end-page: 90 ident: CR28 article-title: On the bounds for the spectral norm of particular matrices with Fibonacci and Lucas numbers publication-title: Int J Adv Appl Math Mech – volume: 3 start-page: 5 issue: 1 year: 1994 end-page: 28 ident: CR35 article-title: Learning and evolution in neural networks publication-title: Adapt Behav doi: 10.1177/105971239400300102 – volume: 49 start-page: 453 year: 2016 ident: CR40 article-title: A computational approach based on the -constraint method in multi-objective optimization problems publication-title: Adv Appl Stat – ident: CR29 – volume: 3 start-page: 257 issue: 2 year: 2015 end-page: 263 ident: CR36 article-title: On the bounds and norms of a particular hadamard exponential matrix publication-title: Appl Math Eng, Manag Technol – volume: 24 start-page: 766 issue: 2 year: 2014 end-page: 794 ident: CR53 article-title: On the Moreau–Yosida regularization of the vector k-norm related functions publication-title: SIAM J Optim doi: 10.1137/110827144 – volume: 14 start-page: 19 issue: 1 year: 2020 end-page: 36 ident: CR22 article-title: Feature selection in SVM via polyhedral k-norm publication-title: Optim Lett doi: 10.1007/s11590-019-01482-1 – ident: CR25 – volume: 3 start-page: 1289 year: 2003 end-page: 1305 ident: CR15 article-title: An extensive empirical study of feature selection metrics for text classification publication-title: J Mach Learn Res – volume: 10 start-page: 424 issue: 6 year: 2021 ident: CR42 article-title: Machine learning and geo-based multi-criteria decision support systems in analysis of complex problems publication-title: ISPRS Int J Geo Inf doi: 10.3390/ijgi10060424 – volume: 2 start-page: 321 issue: 3 year: 1992 end-page: 335 ident: CR50 article-title: Linear best approximation using a class of polyhedral norms publication-title: Numer Algorithms doi: 10.1007/BF02139472 – volume: 10 start-page: 188 issue: 1 year: 2022 end-page: 196 ident: CR37 article-title: Some special matrices with harmonic numbers publication-title: Konuralp J Math – volume: 3 start-page: 713 issue: 06 year: 1981 end-page: 714 ident: CR49 article-title: Remote sensing: the quantitative approach publication-title: IEEE Trans Pattern Anal Mach Intell doi: 10.1109/TPAMI.1981.4767177 – volume: 8 start-page: 631 issue: 3 year: 1998 end-page: 657 ident: CR10 article-title: Normal-boundary intersection—a new method for generating the pareto surface in nonlinear multicriteria optimization problems publication-title: SIAM J Optim doi: 10.1137/S1052623496307510 – ident: CR32 – ident: CR5 – volume: 5 start-page: 19 year: 2011 end-page: 53 ident: CR2 article-title: Convex optimization with sparsity-inducing norms publication-title: Optim Mach Learn – volume: 323 start-page: 533 issue: 6088 year: 1986 end-page: 536 ident: CR46 article-title: Learning representations by back-propagating errors publication-title: Nature doi: 10.1038/323533a0 – volume: 169 start-page: 141 issue: 1 year: 2018 end-page: 176 ident: CR24 article-title: Dc formulations and algorithms for sparse optimization problems publication-title: Math Program doi: 10.1007/s10107-017-1181-0 – year: 2005 ident: CR13 publication-title: Multicriteria optimization – ident: CR18 – ident: CR43 – volume: 2 start-page: 41 issue: 2004 year: 2004 ident: CR26 article-title: A comprehensive foundation publication-title: Neural Netw – volume: 21 start-page: 565 issue: 4 year: 2006 end-page: 582 ident: CR39 article-title: Global optimization toolbox for maple: an introduction with illustrative applications publication-title: Optim Methods Softw doi: 10.1080/10556780600628212 – volume: 9 start-page: 15 year: 2013 end-page: 26 ident: CR1 article-title: Feature subset selection using differential evolution and a wheel based search strategy publication-title: Swarm Evol Comput doi: 10.1016/j.swevo.2012.09.003 – year: 2000 ident: CR9 publication-title: An introduction to support vector machines and other kernel-based learning methods doi: 10.1017/CBO9780511801389 – volume: 60 start-page: 1091 issue: 8–9 year: 2011 end-page: 1104 ident: CR12 article-title: A new scalarization and numerical method for constructing the weak pareto front of multi-objective optimization problems publication-title: Optimization doi: 10.1080/02331934.2011.587006 – ident: CR14 – volume: 57 start-page: 4686 issue: 12 year: 2009 end-page: 4698 ident: CR17 article-title: Recovering sparse signals with a certain family of nonconvex penalties and DC programming publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2009.2026004 – ident: CR33 – volume: 272 start-page: 61 issue: 1 year: 2019 end-page: 77 ident: CR7 article-title: Finding a representative nondominated set for multi-objective mixed integer programs publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2018.06.012 – ident: CR6 – volume: 33 start-page: 2149 issue: 7 year: 2019 end-page: 2179 ident: CR11 article-title: Efficient algorithms for solving nonlinear fractional programming problems publication-title: Filomat doi: 10.2298/FIL1907149D – ident: CR27 – volume: 22 start-page: 159 issue: 1 year: 2012 end-page: 186 ident: CR52 article-title: Accelerated block-coordinate relaxation for regularized optimization publication-title: SIAM J Optim doi: 10.1137/100808563 – volume: 31 start-page: 226 issue: 3 year: 2010 end-page: 233 ident: CR8 article-title: A rough set approach to feature selection based on ant colony optimization publication-title: Pattern Recogn Lett doi: 10.1016/j.patrec.2009.10.013 – volume: 290 start-page: 807 issue: 3 year: 2021 end-page: 828 ident: CR16 article-title: Optimization problems for machine learning: a survey publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2020.08.045 – volume: 43 start-page: 580 issue: 2 year: 2018 end-page: 597 ident: CR20 article-title: Minimizing piecewise-concave functions over polyhedra publication-title: Math Oper Res doi: 10.1287/moor.2017.0873 – volume: 7 start-page: 33 issue: 1 year: 1999 end-page: 70 ident: CR45 article-title: Extensions of Dinkelbach’s algorithm for solving non-linear fractional programming problems publication-title: TOP doi: 10.1007/BF02564711 – volume: 44 start-page: 813 issue: 2 year: 2016 end-page: 852 ident: CR4 article-title: Best subset selection via a modern optimization lens publication-title: Ann Stat doi: 10.1214/15-AOS1388 – volume: 151 start-page: 63 issue: 1 year: 2015 end-page: 87 ident: CR38 article-title: Sparse learning via Boolean relaxations publication-title: Math Program doi: 10.1007/s10107-015-0894-1 – volume: 27 start-page: 2034 issue: 3 year: 2017 end-page: 2060 ident: CR48 article-title: A unified view of exact continuous penalties for ell\_2- ell\_0 minimization publication-title: SIAM J Optim doi: 10.1137/16M1059333 – ident: CR31 – volume: 181 start-page: 1 issue: 12 year: 2018 end-page: 5 ident: CR47 article-title: A novel solution approach using linearization technique for nonlinear programming problems publication-title: Int J Comput Appl – ident: CR34 – volume: 39 start-page: 7483 issue: 23–24 year: 2015 end-page: 7498 ident: CR23 article-title: A new scalarization method for finding the efficient frontier in non-convex multi-objective problems publication-title: Appl Math Model doi: 10.1016/j.apm.2015.03.022 – ident: CR41 – volume: 71 start-page: 37 issue: 1 year: 2018 end-page: 55 ident: CR21 article-title: Minimizing nonsmooth DC functions via successive dc piecewise-affine approximations publication-title: J Global Optim doi: 10.1007/s10898-017-0568-z – volume: 14 start-page: 19 issue: 1 year: 2020 ident: 8839_CR22 publication-title: Optim Lett doi: 10.1007/s11590-019-01482-1 – ident: 8839_CR31 – ident: 8839_CR29 – volume-title: Multicriteria optimization year: 2005 ident: 8839_CR13 – ident: 8839_CR41 – volume: 10 start-page: 188 issue: 1 year: 2022 ident: 8839_CR37 publication-title: Konuralp J Math – volume: 22 start-page: 159 issue: 1 year: 2012 ident: 8839_CR52 publication-title: SIAM J Optim doi: 10.1137/100808563 – volume: 44 start-page: 813 issue: 2 year: 2016 ident: 8839_CR4 publication-title: Ann Stat doi: 10.1214/15-AOS1388 – volume: 87 start-page: 137 year: 2017 ident: 8839_CR19 publication-title: Comput Oper Res doi: 10.1016/j.cor.2017.06.001 – volume: 21 start-page: 565 issue: 4 year: 2006 ident: 8839_CR39 publication-title: Optim Methods Softw doi: 10.1080/10556780600628212 – volume: 3 start-page: 5 issue: 1 year: 1994 ident: 8839_CR35 publication-title: Adapt Behav doi: 10.1177/105971239400300102 – volume: 60 start-page: 1091 issue: 8–9 year: 2011 ident: 8839_CR12 publication-title: Optimization doi: 10.1080/02331934.2011.587006 – volume: 290 start-page: 807 issue: 3 year: 2021 ident: 8839_CR16 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2020.08.045 – volume: 43 start-page: 580 issue: 2 year: 2018 ident: 8839_CR20 publication-title: Math Oper Res doi: 10.1287/moor.2017.0873 – ident: 8839_CR27 doi: 10.1109/CDC.2014.7040063 – volume: 3 start-page: 257 issue: 2 year: 2015 ident: 8839_CR36 publication-title: Appl Math Eng, Manag Technol – volume: 3 start-page: 713 issue: 06 year: 1981 ident: 8839_CR49 publication-title: IEEE Trans Pattern Anal Mach Intell doi: 10.1109/TPAMI.1981.4767177 – volume: 39 start-page: 7483 issue: 23–24 year: 2015 ident: 8839_CR23 publication-title: Appl Math Model doi: 10.1016/j.apm.2015.03.022 – ident: 8839_CR32 doi: 10.1016/B978-1-55860-335-6.50023-4 – volume: 49 start-page: 453 year: 2016 ident: 8839_CR40 publication-title: Adv Appl Stat – volume: 8 start-page: 631 issue: 3 year: 1998 ident: 8839_CR10 publication-title: SIAM J Optim doi: 10.1137/S1052623496307510 – volume: 2 start-page: 41 issue: 2004 year: 2004 ident: 8839_CR26 publication-title: Neural Netw – volume: 5 start-page: 19 year: 2011 ident: 8839_CR2 publication-title: Optim Mach Learn – volume: 10 start-page: 424 issue: 6 year: 2021 ident: 8839_CR42 publication-title: ISPRS Int J Geo Inf doi: 10.3390/ijgi10060424 – ident: 8839_CR6 doi: 10.1109/CEC.2012.6256452 – volume: 31 start-page: 226 issue: 3 year: 2010 ident: 8839_CR8 publication-title: Pattern Recogn Lett doi: 10.1016/j.patrec.2009.10.013 – ident: 8839_CR14 – volume: 9 start-page: 15 year: 2013 ident: 8839_CR1 publication-title: Swarm Evol Comput doi: 10.1016/j.swevo.2012.09.003 – ident: 8839_CR5 – volume: 57 start-page: 4686 issue: 12 year: 2009 ident: 8839_CR17 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2009.2026004 – volume: 3 start-page: 1289 year: 2003 ident: 8839_CR15 publication-title: J Mach Learn Res – ident: 8839_CR18 doi: 10.1137/21M1391481 – volume: 27 start-page: 2034 issue: 3 year: 2017 ident: 8839_CR48 publication-title: SIAM J Optim doi: 10.1137/16M1059333 – volume: 3 start-page: 82 issue: 4 year: 2016 ident: 8839_CR28 publication-title: Int J Adv Appl Math Mech – volume: 46 start-page: 467 issue: 3 year: 2010 ident: 8839_CR44 publication-title: Comput Optim Appl doi: 10.1007/s10589-008-9202-9 – ident: 8839_CR25 doi: 10.1007/978-3-540-71618-1_27 – ident: 8839_CR43 – volume: 181 start-page: 1 issue: 12 year: 2018 ident: 8839_CR47 publication-title: Int J Comput Appl – volume: 71 start-page: 37 issue: 1 year: 2018 ident: 8839_CR21 publication-title: J Global Optim doi: 10.1007/s10898-017-0568-z – volume: 4 start-page: 47 year: 2015 ident: 8839_CR30 publication-title: Appl Comput Math doi: 10.11648/j.acm.20150402.13 – volume: 151 start-page: 63 issue: 1 year: 2015 ident: 8839_CR38 publication-title: Math Program doi: 10.1007/s10107-015-0894-1 – ident: 8839_CR33 doi: 10.1007/978-3-642-99789-1_13 – volume: 7 start-page: 33 issue: 1 year: 1999 ident: 8839_CR45 publication-title: TOP doi: 10.1007/BF02564711 – volume-title: An introduction to support vector machines and other kernel-based learning methods year: 2000 ident: 8839_CR9 doi: 10.1017/CBO9780511801389 – ident: 8839_CR34 doi: 10.1145/1569901.1570040 – volume: 323 start-page: 533 issue: 6088 year: 1986 ident: 8839_CR46 publication-title: Nature doi: 10.1038/323533a0 – volume-title: Convex analysis and monotone operator theory in Hilbert spaces year: 2011 ident: 8839_CR3 doi: 10.1007/978-1-4419-9467-7 – volume: 169 start-page: 141 issue: 1 year: 2018 ident: 8839_CR24 publication-title: Math Program doi: 10.1007/s10107-017-1181-0 – volume: 33 start-page: 2149 issue: 7 year: 2019 ident: 8839_CR11 publication-title: Filomat doi: 10.2298/FIL1907149D – ident: 8839_CR51 – volume: 272 start-page: 61 issue: 1 year: 2019 ident: 8839_CR7 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2018.06.012 – volume: 2 start-page: 321 issue: 3 year: 1992 ident: 8839_CR50 publication-title: Numer Algorithms doi: 10.1007/BF02139472 – volume: 24 start-page: 766 issue: 2 year: 2014 ident: 8839_CR53 publication-title: SIAM J Optim doi: 10.1137/110827144 |
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| SubjectTerms | Algorithms Artificial Intelligence Classification Computational Intelligence Control Engineering Feature selection Machine learning Mathematical Logic and Foundations Mathematical programming Mechatronics Mixed integer Multiple objective analysis Nonlinear programming Norms Objectives Optimization Parameter estimation Robotics Sparsity Support vector machines |
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| Title | New mixed integer fractional programming problem and some multi-objective models for sparse optimization |
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