Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming
Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
M.-Alizadeh, Benyamin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
Polynomial nonlinear programming |
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| Anmerkung: |
© Iranian Mathematical Society 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Bulletin of the Iranian Mathematical Society - Singapore : Springer Singapore, 2001, 45(2019), 6 vom: 18. März, Seite 1585-1603 |
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| Übergeordnetes Werk: |
volume:45 ; year:2019 ; number:6 ; day:18 ; month:03 ; pages:1585-1603 |
| Links: |
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| DOI / URN: |
10.1007/s41980-019-00217-3 |
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| Katalog-ID: |
SPR038362937 |
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| 100 | 1 | |a M.-Alizadeh, Benyamin |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming |
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| 520 | |a Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. | ||
| 650 | 4 | |a Polynomial nonlinear programming |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multiparametric polynomial nonlinear programming |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Eigenvalue system |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Gröbner basis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Comprehensive Gröbner system |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Basiri, Abdolali |4 aut | |
| 700 | 1 | |a Rahmany, Sajjad |0 (orcid)0000-0001-6871-151X |4 aut | |
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10.1007/s41980-019-00217-3 doi (DE-627)SPR038362937 (SPR)s41980-019-00217-3-e DE-627 ger DE-627 rakwb eng M.-Alizadeh, Benyamin verfasserin aut Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 Basiri, Abdolali aut Rahmany, Sajjad (orcid)0000-0001-6871-151X aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 6 vom: 18. März, Seite 1585-1603 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:6 day:18 month:03 pages:1585-1603 https://dx.doi.org/10.1007/s41980-019-00217-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 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_2008 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 6 18 03 1585-1603 |
| spelling |
10.1007/s41980-019-00217-3 doi (DE-627)SPR038362937 (SPR)s41980-019-00217-3-e DE-627 ger DE-627 rakwb eng M.-Alizadeh, Benyamin verfasserin aut Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 Basiri, Abdolali aut Rahmany, Sajjad (orcid)0000-0001-6871-151X aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 6 vom: 18. März, Seite 1585-1603 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:6 day:18 month:03 pages:1585-1603 https://dx.doi.org/10.1007/s41980-019-00217-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 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_2008 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 6 18 03 1585-1603 |
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10.1007/s41980-019-00217-3 doi (DE-627)SPR038362937 (SPR)s41980-019-00217-3-e DE-627 ger DE-627 rakwb eng M.-Alizadeh, Benyamin verfasserin aut Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 Basiri, Abdolali aut Rahmany, Sajjad (orcid)0000-0001-6871-151X aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 6 vom: 18. März, Seite 1585-1603 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:6 day:18 month:03 pages:1585-1603 https://dx.doi.org/10.1007/s41980-019-00217-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 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_2008 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 6 18 03 1585-1603 |
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10.1007/s41980-019-00217-3 doi (DE-627)SPR038362937 (SPR)s41980-019-00217-3-e DE-627 ger DE-627 rakwb eng M.-Alizadeh, Benyamin verfasserin aut Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 Basiri, Abdolali aut Rahmany, Sajjad (orcid)0000-0001-6871-151X aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 6 vom: 18. März, Seite 1585-1603 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:6 day:18 month:03 pages:1585-1603 https://dx.doi.org/10.1007/s41980-019-00217-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 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_2008 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 6 18 03 1585-1603 |
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10.1007/s41980-019-00217-3 doi (DE-627)SPR038362937 (SPR)s41980-019-00217-3-e DE-627 ger DE-627 rakwb eng M.-Alizadeh, Benyamin verfasserin aut Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 Basiri, Abdolali aut Rahmany, Sajjad (orcid)0000-0001-6871-151X aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 6 vom: 18. März, Seite 1585-1603 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:6 day:18 month:03 pages:1585-1603 https://dx.doi.org/10.1007/s41980-019-00217-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 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_2008 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_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_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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 6 18 03 1585-1603 |
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M.-Alizadeh, Benyamin |
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M.-Alizadeh, Benyamin misc Polynomial nonlinear programming misc Multiparametric polynomial nonlinear programming misc Eigenvalue system misc Gröbner basis misc Comprehensive Gröbner system Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming |
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Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming Polynomial nonlinear programming (dpeaa)DE-He213 Multiparametric polynomial nonlinear programming (dpeaa)DE-He213 Eigenvalue system (dpeaa)DE-He213 Gröbner basis (dpeaa)DE-He213 Comprehensive Gröbner system (dpeaa)DE-He213 |
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applying gröbner basis method to multiparametric polynomial nonlinear programming |
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Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming |
| abstract |
Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. © Iranian Mathematical Society 2019 |
| abstractGer |
Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. © Iranian Mathematical Society 2019 |
| abstract_unstemmed |
Abstract In this paper, we present first a new algorithm based on Gröbner basis to analyze and/or solve a convex polynomial nonlinear programming problem that is a convex nonlinear programming in which the objective and constraints are algebraic polynomials. The main efficiency of our algorithm is that there is no need to compute feasible points to find the optimum value. Next, we generalize our results to analyze and/or solvemultiparametric convex polynomial nonlinear programming problems. The mainproperty of this method is that it preserves the parametric scheme of theproblem until the end of the algorithm. Even the output of our algorithm depends onparameters and so one can present the optimum value and optimizer points as afunction on parameters. To show the ability of this algorithm, we will state two applied examples: the problem of minimizing the expense of forage in a chicken farm with unpredictable price of forage and the number of chickens, and an optimal control problem in model predictive control. The presented algorithms in this paper are all implemented in the Maple software. © Iranian Mathematical Society 2019 |
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Applying Gröbner Basis Method to Multiparametric Polynomial Nonlinear Programming |
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https://dx.doi.org/10.1007/s41980-019-00217-3 |
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Basiri, Abdolali Rahmany, Sajjad |
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10.1007/s41980-019-00217-3 |
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