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A Method of Two New Augmented Lagrange Multiplier Versions for Solving Constrained Problems

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  • Hamsa Th. Saeed Chilmeran
  • Eman T. Hamed
  • Huda I. Ahmed
  • Abbas Y. Al-Bayati
  • Frank Werner

Abstract

One of the more restrictive methods of improvement is the augmented Lagrange method. Two versions are built in the external framework and the internal framework of the proposed method. The first basic version of the proposed algorithm includes a new derivation of Lagrange multiples and different penalty criteria, and the second version is the internal framework in which the unconstrained algorithm known as the conjugate gradient (CG) method was incorporated; also, a new parameter was derived in the search direction. The numerical results are indicative of the stability, efficiency, and speed of the proposed algorithm, based on performance profiles provided by Dolan and More.

Suggested Citation

  • Hamsa Th. Saeed Chilmeran & Eman T. Hamed & Huda I. Ahmed & Abbas Y. Al-Bayati & Frank Werner, 2022. "A Method of Two New Augmented Lagrange Multiplier Versions for Solving Constrained Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-6, April.
    • Handle: RePEc:hin:jijmms:3527623
    DOI: 10.1155/2022/3527623
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