Mathematical Programming Computational for Solving NP-Hardness Problem
In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the tw...
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| Published in | Journal of physics. Conference series Vol. 1818; no. 1; p. 12137 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Bristol
IOP Publishing
01.03.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1742-6588 1742-6596 |
| DOI | 10.1088/1742-6596/1818/1/012137 |
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| Abstract | In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the two methods which is Penalty and Augmented Lagrangian methods base on the numerical result. Moreover, we tested the K-cluster problem and found the Augmented Lagrangian Method faster than Penalty method. Finally, our research is not just focus on the numerical computational but also improving the theoretical converges properties. |
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| AbstractList | In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the two methods which is Penalty and Augmented Lagrangian methods base on the numerical result. Moreover, we tested the K-cluster problem and found the Augmented Lagrangian Method faster than Penalty method. Finally, our research is not just focus on the numerical computational but also improving the theoretical converges properties. |
| Author | Al-Jilawi, Ahmed Sabah Alridha, Ahmed |
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| Cites_doi | 10.1023/A:1017571111854 10.1137/S1052623400382467 10.1007/s10957-017-1108-1 10.1007/BF00927673 10.1137/16M1107103 10.1021/i160020a009 10.1007/s11228-018-0497-0 10.1145/261342.571216 10.1007/BF01585731 |
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| Copyright | 2021. This work is published under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.1088/1742-6596/1818/1/012137 |
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| References | Dempe (JPCS_1818_1_012137bib7) 2001; 110 Hochba (JPCS_1818_1_012137bib11) 1997; 28 Bertsekas (JPCS_1818_1_012137bib8) 1999 Buriol (JPCS_1818_1_012137bib10) 2020 Du (JPCS_1818_1_012137bib9) 2017; 173 Belloni (JPCS_1818_1_012137bib3) 2005 Burer (JPCS_1818_1_012137bib6) 2002; 12 Bertsekas (JPCS_1818_1_012137bib5) 2014 Kiwiel (JPCS_1818_1_012137bib18) 1990; 46 King (JPCS_1818_1_012137bib17) 1966; 5 Al-Jilawi (JPCS_1818_1_012137bib1) 2019 Bertsekas (JPCS_1818_1_012137bib4) 2015 Jumaa (JPCS_1818_1_012137bib12) 2020; 1591 Joki (JPCS_1818_1_012137bib15) 2013 Schoenauer (JPCS_1818_1_012137bib2) 1996 Hestenes (JPCS_1818_1_012137bib13) 1969; 4 de Oliveira (JPCS_1818_1_012137bib14) 2019; 27 Kanzow (JPCS_1818_1_012137bib16) 2018; 56 |
| References_xml | – volume: 110 start-page: 265 year: 2001 ident: JPCS_1818_1_012137bib7 article-title: Bundle trust-region algorithm for bilinear bilevel programming publication-title: Journal of Optimization Theory and Applications doi: 10.1023/A:1017571111854 – volume: 12 start-page: 503 year: 2002 ident: JPCS_1818_1_012137bib6 article-title: Rank-two relaxation heuristics for max-cut and other binary quadratic programs publication-title: SIAM Journal on Optimization doi: 10.1137/S1052623400382467 – volume: 173 start-page: 908 year: 2017 ident: JPCS_1818_1_012137bib9 article-title: Rate of convergence of the bundle method publication-title: Journal of Optimization Theory and Applications doi: 10.1007/s10957-017-1108-1 – year: 2015 ident: JPCS_1818_1_012137bib4 – start-page: 40 year: 2020 ident: JPCS_1818_1_012137bib10 article-title: THE GUIDE TO NP-COMPLETENESS IS 40 YEARS OLD: AN HOMAGE TO DAVID S. JOHNSON – start-page: 11 year: 2005 ident: JPCS_1818_1_012137bib3 – volume: 4 start-page: 303 year: 1969 ident: JPCS_1818_1_012137bib13 article-title: Multiplier and gradient methods publication-title: Journal of optimization theory and applications doi: 10.1007/BF00927673 – volume: 56 start-page: 272 year: 2018 ident: JPCS_1818_1_012137bib16 article-title: An augmented Lagrangian method for optimization problems in Banach spaces publication-title: SIAM Journal on Control and Optimization doi: 10.1137/16M1107103 – volume: 5 start-page: 484 year: 1966 ident: JPCS_1818_1_012137bib17 article-title: Necessary and sufficient conditions for inequality constrained extreme values publication-title: Industrial & Engineering Chemistry Fundamentals doi: 10.1021/i160020a009 – year: 2019 ident: JPCS_1818_1_012137bib1 – year: 2013 ident: JPCS_1818_1_012137bib15 article-title: Nonsmooth Optimization: Bundle Methods – volume: 27 start-page: 895 year: 2019 ident: JPCS_1818_1_012137bib14 article-title: An inertial algorithm for DC programming publication-title: Set-Valued and Variational Analysis doi: 10.1007/s11228-018-0497-0 – year: 1999 ident: JPCS_1818_1_012137bib8 – start-page: 245 year: 1996 ident: JPCS_1818_1_012137bib2 – year: 2014 ident: JPCS_1818_1_012137bib5 – volume: 1591 year: 2020 ident: JPCS_1818_1_012137bib12 article-title: Solving Max-Cut Optimization Problem publication-title: Journal of Physics: Conference Series – volume: 28 start-page: 40 year: 1997 ident: JPCS_1818_1_012137bib11 article-title: Approximation algorithms for NP-hard problems publication-title: ACM Sigact News doi: 10.1145/261342.571216 – volume: 46 start-page: 105 year: 1990 ident: JPCS_1818_1_012137bib18 article-title: Proximity control in bundle methods for convex nondifferentiable minimization publication-title: Mathematical programming doi: 10.1007/BF01585731 |
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| SubjectTerms | Clusters Combinatorial analysis Hardness Mathematical programming Numerical methods Optimization Physics Polynomials |
| Title | Mathematical Programming Computational for Solving NP-Hardness Problem |
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