Collinear Gradients Method for Minimizing Smooth Functions

Victor K. Tolstykh ()
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Victor K. Tolstykh: Donetsk National University

SN Operations Research Forum, 2023, vol. 4, issue 1, 1-13

Abstract: Abstract A new optimization method for unconstrained smooth functions is proposed. It is based on a special form of the necessary optimality condition in the vicinity of the optimum. The method uses the first derivatives of the objective function, while demonstrating convergence as Newton method (second derivatives). Illustrations of how the method works step by step are provided. Algorithms for practical implementation are considered, and numerous test calculations demonstrating the high efficiency of the method are presented.

Keywords: Numerical optimization; Minimization of functions; Gradient; Necessary conditions; 49K10; 49M5; 65K05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-023-00193-9

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