A nonmonotone supermemory gradient algorithm for unconstrained optimization

• Published in: Journal of applied mathematics & computing Vol. 46; no. 1-2; pp. 215 - 235
• Main Authors: Ou, Yigui, Liu, Yuanwen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2014; Springer Nature B.V
• Subjects: Algorithms; Applied mathematics; Computation; Computational mathematics; Computational Mathematics and Numerical Analysis; Convergence; Iterative methods; Mathematical analysis; Mathematical and Computational Engineering; Mathematical models; Mathematics; Mathematics and Statistics; Mathematics of Computing; Matrices (mathematics); Methods; Nonlinear equations; Optimization; Optimization algorithms; Original Research; Studies; Theorems; Theory of Computation; Unconstrained optimization; 90C30; 65K05; Supermemory gradient method; 49M37; Nonmonotone line search; Convergence analysis
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-013-0747-0

This paper presents a nonmonotone supermemory gradient algorithm for unconstrained optimization problems. At each iteration, this proposed method sufficiently uses the previous multi-step iterative information and avoids the storage and computation of matrices associated with the Hessian of objective functions, thus it is suitable to solve large-scale optimization problems and can converge stably. Under some assumptions, the convergence properties of the proposed algorithm are analyzed. Numerical results are also reported to show the efficiency of this proposed method.