A New Descent Algorithm Using the Three-Step Discretization Method for Solving Unconstrained Optimization Problems

Mina Torabi and Mohammad-Mehdi Hosseini
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Mina Torabi: Department of Applied Mathematics, Faculty of Mathematics, Yazd University, P. O. Box 89195-741, Yazd, Iran
Mohammad-Mehdi Hosseini: Department of Applied Mathematics, Faculty of Mathematics, Yazd University, P. O. Box 89195-741, Yazd, Iran

Mathematics, 2018, vol. 6, issue 4, 1-18

Abstract: In this paper, three-step Taylor expansion, which is equivalent to third-order Taylor expansion, is used as a mathematical base of the new descent method. At each iteration of this method, three steps are performed. Each step has a similar structure to the steepest descent method, except that the generalized search direction, step length, and next iterative point are applied. Compared with the steepest descent method, it is shown that the proposed algorithm has higher convergence speed and lower computational cost and storage.

Keywords: unconstrained optimization; line search; three-step discretization method; steepest descent method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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