Numerical Experiment with the Introduction of a Scaling Factor to the Multiplier Method to Solve Constrained Optimization Problems

Adebayo Kayode James, Dele-Rotimi Adejoke Olumide, Adisa Isaac Olabisi, Alabi Taiye John and Ademoroti Albert Olalekan
Additional contact information
Adebayo Kayode James: Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State, Nigeria
Dele-Rotimi Adejoke Olumide: Department of Mathematics, Bamidele Olumilua University of Education, Science, and Technology, Ikere Ekiti, Ekiti State, Nigeria
Adisa Isaac Olabisi: Department of Mathematics, Adeyemi University of Education, Ondo, Ondo State, Nigeria
Alabi Taiye John: Department of Statistics, Kogi State Polytechnic, Lokoja, Kogi State, Nigeria
Ademoroti Albert Olalekan: Department of Physics, Bamidele Olumilua University of Education, Science, and Technology, Ikere Ekiti, Ekiti State, Nigeria

International Journal of Research and Innovation in Applied Science, 2025, vol. 10, issue 7, 1417-1424

Abstract: This paper discusses the intertwining of the Conjugate Gradient Method (CGM) as a scaling factor for Newton’s algorithm, which is employed to determine the solution of the constrained optimization problems. The constrained problem has to be converted to an unconstrained problem via the multiplier method, after which a scaling is introduced to Conjugate Gradient Method (CGM) of Hestenes and Stiefel that forces the problem to collapse toward the resulting equation quickly. Newton’s algorithm, which was embedded in the algorithm of the multiplier method, was used to carry out the minimization process. At each descent direction search, a formulated dynamic is used to update the Lagrange multiplier, such that this is done at each one-dimensional search until the optimality is reached. The use of this method was not limited to optimization problems alone, it has been extended to optimal control problems of the Lagrange and the Meyer forms, with a huge success recorded when the results obtained were compared with results of other existing methods.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.rsisinternational.org/journals/ijrias/ ... ssue-7/1417-1424.pdf (application/pdf)
https://rsisinternational.org/journals/ijrias/arti ... timization-problems/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bjf:journl:v:10:y:2025:i:7:p:1417-1424

Access Statistics for this article

International Journal of Research and Innovation in Applied Science is currently edited by Dr. Renu Malsaria

More articles in International Journal of Research and Innovation in Applied Science from International Journal of Research and Innovation in Applied Science (IJRIAS)
Bibliographic data for series maintained by Dr. Renu Malsaria ().