A class of nonmonotone Armijo-type line search method for unconstrained optimization

Ahookhosh, Masoud; Amini, Keyvan; Bahrami, Somayeh

doi:10.1080/02331934.2011.641126

Cited by 26 publications

(27 citation statements)

References 17 publications

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“…Assumption A4 seems to be a little strong [26]. However, if we make this assumption (see [1,2,13], for example): There exists a constant M 0 > 0 such that…”

Section: Remarkmentioning

confidence: 96%

“…The numerical results reported in [36] show that this nonmonotone technique (6) is superior to the nonmonotone technique (5). Based on this nonmonotone technique (6) or its variant, researchers developed some new nonmonotone trust region methods or nonmonotone line search methods for unconstrained optimization problem (1), for example, see [1,13,16,18,35]. Theoretical and computational results show that these methods can improve the efficiency of the nonmonotone methods.…”

Section: Introductionmentioning

confidence: 94%

“…Methods of this type have been proposed in the literature, for instance, see [3,6,14,15,21,25,37] and references therein. Extensive numerical testing experience reported by Brown and Biggs [6] suggests that ODE-based methods for solving problem (1) can in fact be implemented in such a way as to be very competitive with conventional Newton and quasi-Newton algorithms regarding reliability, accuracy and efficiency, especially for highly nonlinear minimization problems with narrow and curved valleys. Among all ODE-based methods mentioned in [6], the most successful algorithm is IMPBOT, which is based on the following initial value problem of linearized steepest descent equations:…”

Section: Introductionmentioning

confidence: 98%

“…Based on these methods, Ou [26] also proposed a hybrid method for solving problem (1), which combines the idea of IMPBOT with the trust region and line search techniques. Subsequently, Ou and Wang [27] further studied ODE methods and developed a hybrid ODE-based method for problem (1), which combines the idea of IMPBOT with the subspace technique and a fixed stepsize. Numerical examples show that the methods in [26,27] are efficient and reliable for small scale optimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…Many approaches for solving problem (1) are iterative methods such as trust region and line search, see [30] for details. Throughout the paper, · denotes the Euclidean norm on R n .…”

Section: Introductionmentioning

confidence: 99%

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A nonmonotone ODE-based method for unconstrained optimization

2014

International Journal of Computer Mathematics

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This paper presents a new hybrid algorithm for unconstrained optimization problems, which combines the idea of the IMPBOT algorithm with the nonmonotone line search technique. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step, via a modified limited-memory BFGS two loop recursion that requires only matrix-vector products, thus reducing the computations and storage. Furthermore, when the trial step is not accepted, the proposed method performs a line search along it using a modified nonmonotone scheme, thus a larger stepsize can be yielded in each line search procedure. Under some reasonable assumptions, the convergence properties of the proposed algorithm are analysed. Numerical results are also reported to show the efficiency of this proposed method.

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“…Assumption A4 seems to be a little strong [26]. However, if we make this assumption (see [1,2,13], for example): There exists a constant M 0 > 0 such that…”

Section: Remarkmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

“…Many approaches for solving problem (1) are iterative methods such as trust region and line search, see [30] for details. Throughout the paper, · denotes the Euclidean norm on R n .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations