Determining the step length in iterations of nonlinear minimization represents a problem that is not uniquely defined. Motivated by such uncertainty in defining step length, our intention was to use the capabilities of neutrosophy in this process. Our idea is to unify the usability and numerous applications of neutrosophic logic and the enormous importance of nonlinear optimization. An improvement of line search iteration for solving unconstrained optimization is proposed using appropriately defined Neutrosophic logic system in determining appropriate step size for the class of descent direction methods. The basic idea is to use an additional parameter that would monitor the behavior of the objective function and, based on that, correct the step length in known optimization methods. Mutual comparison and analysis of generated numerical results reveal better results generated by the suggested iterations compared to analogous available iterations considering the statistical ranking technique. Statistical measures show advantages of fuzzy improvements of considered line search optimization methods.
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27 February 2023
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Hybrid methods, modeling and optimization, complex systems, mathematical models, data mining, computational intelligence
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Stanimirović, P. S., Ivanov, B., Katsikis, V. N., & Mourtas, S. D. (2023). Neutrosophy in Unconstrained Nonlinear Optimization. In P. Stanimorovic, A. A. Stupina, E. Semenkin, & I. V. Kovalev (Eds.), Hybrid Methods of Modeling and Optimization in Complex Systems, vol 1. European Proceedings of Computers and Technology (pp. 131-139). European Publisher. https://doi.org/10.15405/epct.23021.17