AIMS Mathematics (Aug 2024)

An efficient augmented memoryless quasi-Newton method for solving large-scale unconstrained optimization problems

  • Yulin Cheng ,
  • Jing Gao

DOI
https://doi.org/10.3934/math.20241231
Journal volume & issue
Vol. 9, no. 9
pp. 25232 – 25252

Abstract

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In this paper, an augmented memoryless BFGS quasi-Newton method was proposed for solving unconstrained optimization problems. Based on a new modified secant equation, an augmented memoryless BFGS update formula and an efficient optimization algorithm were established. To improve the stability of the numerical experiment, we obtained the scaling parameter by minimizing the upper bound of the condition number. The global convergence of the algorithm was proved, and numerical experiments showed that the algorithm was efficient.

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