A hybrid trust region algorithm for unconstrained optimization

Ou, Yigui

doi:10.1016/j.apnum.2011.03.002

Cited by 9 publications

(11 citation statements)

References 9 publications

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“…Assumption 4.2 is the one usually used in the study of the convergence properties for monotone or nonmonotone methods (for example, see Refs. [11,12,14,[24][25][26][32][33][34] …”

Section: Assumption 41 the Level Setmentioning

confidence: 99%

“…[20][21][22][23][24][25] and references therein. By means of extensive numerical experiments, it has been shown that, when suitably implemented, some ODE-based methods for solving smooth optimization can compare very favorably with conventional optimization algorithms as regards reliability, accuracy and efficiency, especially for highly nonlinear minimization problems with narrow curved valleys, for example, see Refs.…”

Section: Introductionmentioning

confidence: 99%

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An ODE-like nonmonotone method for nonsmooth convex optimization

Lin

2015

J. Appl. Math. Comput.

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Based on the Moreau-Yosida regularization and a modified nonmonotone line search technique, this paper presents an implementable ordinary differentiable equation-like method for solving a possibly nondifferentiable convex minimization problem by converting the original objective function to a once continuously differentiable function. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. Under some reasonable conditions, the proposed method is shown to be globally and superlinearly convergent. Some preliminary numerical results are also reported to show the efficiency of the proposed method.

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“…Assumption 4.2 is the one usually used in the study of the convergence properties for monotone or nonmonotone methods (for example, see Refs. [11,12,14,[24][25][26][32][33][34] …”

Section: Assumption 41 the Level Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An ODE-like nonmonotone method for nonsmooth convex optimization

Lin

2015

J. Appl. Math. Comput.

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“…Nonmonotone hybrid TR algorithm may be regarded as our further research of previous work [26]. The difference between them is that a modified nonmonotone line search (10) is used here instead of a standard Armijo line search, thus a larger stepsize can be obtained in each line search procedure.…”

Section: Remarkmentioning

confidence: 99%

“…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: 97%

“…Therefore, these methods require less cost of computation than classical trust region methods. 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.…”

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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An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Liu

Cui

2017

Comput Optim Appl

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A hybrid trust region algorithm for unconstrained optimization

Cited by 9 publications

References 9 publications

An ODE-like nonmonotone method for nonsmooth convex optimization

An ODE-like nonmonotone method for nonsmooth convex optimization

A nonmonotone ODE-based method for unconstrained optimization

An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

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