Solvability Analysis Of Equality-Constrained Optimization Problems With Nonlinear Functions
DOI:
https://doi.org/10.60787/tnamp.v21.479Keywords:
Necessary conditions, Equality constrained problem, Lagrange Multiplier method, Non-linear functions, Borded Hessian matrixAbstract
This paper attempts fresh review techniques for solving constrained optimization problems with non-linear functions, emphasizing the Lagrange multipliers method. The paper reviews their solvability ability as employed in solving equality-constrained optimization problems. The first and second-order necessary conditions for obtaining optimal solutions are stated and discussed in this paper. The method of Lagrange multiplier was used to solve for optimal points. The work also demonstrates how the Borded Hessian Matrix can be used to determine the optimal solution to non-linear equality constraint problems with many constraints.
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Abdelmonem M. Ibrahim, Mohamed A. Tawhid (2019), A hybridization of differential evolution and monarch butterfly optimization for solving systems of nonlinear equations, Journal of Computational Design and Engineering, PP 354-367.
Cheng Hong, Segen F. Estefen, Marcelo Igor Lourenço and Yuxi Wang (2018). An integrated optimization model for the layout design of a subsea production system. Applied Ocean Research Journal Volume 77, PP 1-13.
Dechao, Xinwei, and Shuai Li (2022), A multi-constrained zeroing neural network for time-dependent nonlinear optimization with application to mobile robot tracking control, Journal of Neurocomputing. Vol460, PP 331-344.
Peter Anuoluwapo and Yanxia Sun (2022) A hybrid constrained Particle Swarm Optimization-Model Predictive Control (CPSO-MPC) algorithm for storage energy management optimization problem in micro-grid, Energy Report journal, University of Johannesburg.
Efor, T.E (2016), optimality conditions for Equality constrained optimization problems: International Journal of Mathematics and Statistics Invention (IJMSI). 4(4), PP 28-33.
Efor T. E, Nwebonyi U. J and, Adum F. L. (2024), Application of Linear Programming for profit Maximization in vegas restaurant and bakery using Simplex method, Journal of Nigerian Association of Mathematical Physics 68(1), PP 107-106.
Mehak and Sankalap (2018). Chaotic grey wolf optimization algorithm for constrained optimization problems, Journal of Computational Design and Engineering, volume 15, PP 458-472.
V. Guliashki et al (2020). Two-stage portfolio risk optimization based on MVO model, International Journal of Reasoning-based Intelligent Systems 12(1):70.
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