New Piecewise Linear Approximation Techniques for Nonlinear Programming Problems
Keywords:
Piecewise Linear Approximation Techniques, Nonlinear Programming ProblemsAbstract
This study presented a novel piecewise linear approximation algorithm for efficiently solving large-scale separable optimisation and concave transportation problems. Six problem sets, three for separable optimisation problems and three for concave transportation problems, were extracted from published articles to demonstrate the effectiveness of the new algorithms. Comparative analysis with existing piecewise linear approximation PLA methods demonstrates that the new approaches achieve higher accuracy, reduced computational time, and improved stability in handling complex constraints. The findings suggest that the newly developed techniques
can serve as a valuable tool for researchers and practitioners in optimisation, offering a balance between precision and computational efficiency. The results show significant reductions in the standard error of the mean for goodness-of-fit measures, indicating enhanced reliability and scalability. The study concludes that the techniques developed and employed contributed to the advancement of computational optimisation techniques, providing a robust and efficient solution for practitioners and researchers tackling large-scale separable optimisation and concave transportation problems.
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