Memoryless quasi-Newton-type methods via some weak secant relations for large-scale unconstrained optimization

• Published in: Journal of inequalities and applications Vol. 2024; no. 1; pp. 155 - 17
• Main Authors: Lim, Keat Hee, Leong, Wah June
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 05.12.2024; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Approximation; Armijo line search; Control and Optimization in Sustainability Applications; Convergence; Iterative methods; Large-scale optimization; Least-change updating scheme; Mathematics; Mathematics and Statistics; Optimization; Quasi Newton methods; Quasi-Newton-type methods; Searching; Symmetry; Weak secant relations; Armijo line search; Quasi-Newton-type methods; Large-scale optimization; Least-change updating scheme; Weak secant relations
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-024-03240-z

This article presents two variants of memoryless quasi-Newton methods with backtracking line search for large-scale unconstrained minimization. These updating methods are derived by means of a least-change updating strategy subjected to some weaker form of secant relation obtained by projecting the secant equation onto the search direction. In such a setting, the search direction can be computed without the need of calculation and storage of matrices. We establish the convergence properties for these methods, and their performance is tested on a large set of test functions by comparing with standard methods of similar computational cost and storage requirement. Our numerical results indicate that significant improvement has been achieved with respect to iteration counts and number of function evaluations.