A limited memory BFGS-type method for large-scale unconstrained optimization

Xiao, Yunhai; Wei, Zengxin; Wang, Zhiguo

doi:10.1016/j.camwa.2008.01.028

Cited by 68 publications

(25 citation statements)

References 21 publications

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“…Thus, L-BFGS has attracted considerable attention and has been used to solve many practical problems. For further information, see [35][36][37] for general methods and [38,39] for applications.…”

Section: Limited Memory Bfgs Methodsmentioning

confidence: 99%

A hybrid approach to constrained global optimization

Liu

Zhang²,

et al. 2016

Applied Soft Computing

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a b s t r a c tIn this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.

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Section: Limited Memory Bfgs Methodsmentioning

confidence: 99%

A hybrid approach to constrained global optimization

Liu

Zhang²,

et al. 2016

Applied Soft Computing

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“…The superlinear convergence theorem of the corresponding BFGS method was established in [38]. Moreover, the work of [38] was extended to deal with large-scale problems in a limited memory scheme in [40]. The reported numerical results show that this extension is beneficial to the performance of the algorithm.…”

Section: Introductionmentioning

confidence: 92%

A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems

Yuan

Wei

2015

J. Appl. Math. Comput.

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It is well-known that nonlinear conjugate gradient (CG) methods are preferred to solve large-scale smooth optimization problems due to their simplicity and low storage. However, the CG methods for nonsmooth optimization have not been studied. In this paper, a modified Polak-Ribière-Polyak CG algorithm which combines with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The search direction of the given method not only possesses the sufficiently descent property but also belongs to a trust region. Moreover, the search direction has not only the gradients information but also the functions information. The global convergence of the presented algorithm is established under suitable conditions. Numerical results show that the given method is competitive to other three methods.

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“…Numerical studies show that methods based on the L-BFGS updating rule are more effective in practice, see e.g. [7,9,24,26,30]. Indeed, the L-BFGS method is the winner on many classes of problems and competes with truncated Newton methods [14] on a variety of large-scale nonlinear problems [26].…”

Section: Introductionmentioning

confidence: 97%

A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems

Tarzanagh

Peyghami

2015

J Glob Optim

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In the framework of large-scale optimization problems, the standard BFGS method is not affordable due to memory constraints. The so-called limited-memory BFGS (L-BFGS) method is an adaption of the BFGS method for large-scale settings. However, the standard BFGS method and therefore the standard L-BFGS method only use the gradient information of the objective function and neglect function values. In this paper, we propose a new regularized L-BFGS method for solving large scale unconstrained optimization problems in which more available information from the function and gradient values are employed to approximate the curvature of the objective function. The proposed method utilizes a class of modified quasi-Newton equations in order to achieve higher order accuracy in approximating the second order curvature of the objective function. Under some standard assumptions, we provide the global convergence property of the new method. In order to provide an efficient method for finding global minima of a continuously differentiable function, a hybrid algorithm that combines a genetic algorithm (GA) with the new proposed regularized L-BFGS method has been proposed. This combination leads the iterates to a stationary point of the objective function with higher chance of being global minima. Numerical results show the efficiency and robustness of the new proposed regularized L-BFGS and its hybridized version with GA in practice.

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A limited memory BFGS-type method for large-scale unconstrained optimization

Cited by 68 publications

References 21 publications

A hybrid approach to constrained global optimization

A hybrid approach to constrained global optimization

A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems

A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems

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