Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)

Samson Adebayo Olorunsola; Temitayo Emmanuel Olaosebikan; Kayode James Adebayo

doi:doi:10.11648/j.ajam.20140206.15

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Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)

Samson Adebayo Olorunsola, Temitayo Emmanuel Olaosebikan, Kayode James Adebayo

Published in American Journal of Applied Mathematics (Volume 2, Issue 6)

Received: 21 December 2014 Accepted: 25 December 2014 Published: 6 January 2015

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Abstract

In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.ajam.20140206.15
Page(s)	221-226
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Lagrange Multiplier Method, Constrained Optimization Problem, Conjugate Gradient Method, Numerical Experiments of the Lagrange Multiplier Conjugate Gradient Method

References

[1]	RAO, S. S., (1978), Optimization Theory and Applications, Willy and Sons.
[2]	THOMAS, F.E., and DAVID, M.H., (2001), Optimization of Chemical Processes, McGraw Hill
[3]	IGOR, G., STEPHEN, G. N. and ARIELA, S., (2009), Linear and Nonlinear Optimization, George Mason University, Fairfax, Virginia, SIAM, Philadelphia.
[4]	David, G. Hull, (2003), Optimal Control Theory for Applications, Mechanical Engineering Series, Springer-Verlag, New York, Inc., 175 Fifth Avenue, New York, NY 10010.
[5]	Bersekas, D. P, (1982), Constrained Optimization and Lagrange Multipliers Method, Academic Press, Inc.
[6]	Rockafellar, R. T., (2005), Multiplier Method of Hestenes and Powell applied to convex Programming, Journal of Optimization Theory and Applications, Vol. 4, No. 4.
[7]	Triphath S. S and Narenda K. S, (1972), Constrained Optimization Problems Using Multiplier Methods, Journal of Optimization Theory and Applications: Vol. 9, No. 1.

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APA Style

Samson Adebayo Olorunsola, Temitayo Emmanuel Olaosebikan, Kayode James Adebayo. (2015). Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). American Journal of Applied Mathematics, 2(6), 221-226. https://doi.org/10.11648/j.ajam.20140206.15

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ACS Style

Samson Adebayo Olorunsola; Temitayo Emmanuel Olaosebikan; Kayode James Adebayo. Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). Am. J. Appl. Math. 2015, 2(6), 221-226. doi: 10.11648/j.ajam.20140206.15

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AMA Style

Samson Adebayo Olorunsola, Temitayo Emmanuel Olaosebikan, Kayode James Adebayo. Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). Am J Appl Math. 2015;2(6):221-226. doi: 10.11648/j.ajam.20140206.15

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@article{10.11648/j.ajam.20140206.15,
  author = {Samson Adebayo Olorunsola and Temitayo Emmanuel Olaosebikan and Kayode James Adebayo},
  title = {Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {221-226},
  doi = {10.11648/j.ajam.20140206.15},
  url = {https://doi.org/10.11648/j.ajam.20140206.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.15},
  abstract = {In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.},
 year = {2015}
}

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TY  - JOUR
T1  - Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)
AU  - Samson Adebayo Olorunsola
AU  - Temitayo Emmanuel Olaosebikan
AU  - Kayode James Adebayo
Y1  - 2015/01/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20140206.15
DO  - 10.11648/j.ajam.20140206.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 221
EP  - 226
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.15
AB  - In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.
VL  - 2
IS  - 6
ER  -

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Author Information

Samson Adebayo Olorunsola

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Temitayo Emmanuel Olaosebikan

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Kayode James Adebayo

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

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Plain Text BibTeX RIS

APA Style

Samson Adebayo Olorunsola, Temitayo Emmanuel Olaosebikan, Kayode James Adebayo. (2015). Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). American Journal of Applied Mathematics, 2(6), 221-226. https://doi.org/10.11648/j.ajam.20140206.15

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ACS Style

Samson Adebayo Olorunsola; Temitayo Emmanuel Olaosebikan; Kayode James Adebayo. Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). Am. J. Appl. Math. 2015, 2(6), 221-226. doi: 10.11648/j.ajam.20140206.15

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AMA Style

Samson Adebayo Olorunsola, Temitayo Emmanuel Olaosebikan, Kayode James Adebayo. Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM). Am J Appl Math. 2015;2(6):221-226. doi: 10.11648/j.ajam.20140206.15

Copy | Download

@article{10.11648/j.ajam.20140206.15,
  author = {Samson Adebayo Olorunsola and Temitayo Emmanuel Olaosebikan and Kayode James Adebayo},
  title = {Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {221-226},
  doi = {10.11648/j.ajam.20140206.15},
  url = {https://doi.org/10.11648/j.ajam.20140206.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.15},
  abstract = {In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)
AU  - Samson Adebayo Olorunsola
AU  - Temitayo Emmanuel Olaosebikan
AU  - Kayode James Adebayo
Y1  - 2015/01/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20140206.15
DO  - 10.11648/j.ajam.20140206.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 221
EP  - 226
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.15
AB  - In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.
VL  - 2
IS  - 6
ER  -

Copy | Download