A nonmonotone supermemory gradient algorithm for unconstrained optimization

Ou, Yigui; Liu, Yuanwen

doi:10.1007/s12190-013-0747-0

Cited by 7 publications

(4 citation statements)

References 40 publications

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“…Notice that this choice of d k is derived from [17]. In what follows we discuss the global convergence and the convergence rate of Algorithm 5.1.…”

Section: Further Discussionmentioning

confidence: 99%

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A memory gradient method for non-smooth convex optimization

Liu

2014

International Journal of Computer Mathematics

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Based on the Moreau-Yosida regularization and a modified line search technique, this paper presents an implementable memory gradient method for solving a possibly non-differentiable convex minimization problem by converting the original objective function to a once continuously differentiable function. A main feature of this proposed method is that at each iteration, it sufficiently uses the previous multi-step iterative information and avoids the storage and computation of some matrices. Moreover, the proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. Under reasonable conditions, the convergence properties of the proposed algorithm are analysed. Preliminary numerical results show that the proposed method is efficient and can be applied to solve large-scale non-smooth optimization problems.

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“…Notice that this choice of d k is derived from [17]. In what follows we discuss the global convergence and the convergence rate of Algorithm 5.1.…”

Section: Further Discussionmentioning

confidence: 99%

“…In what follows we discuss the global convergence and the convergence rate of Algorithm 5.1. To this end, we give the following two properties, whose proofs are essentially the same as Lemmas 1 and 2 in [17], and thus are omitted here.…”

Section: Further Discussionmentioning

confidence: 99%

A memory gradient method for non-smooth convex optimization

Liu

2014

International Journal of Computer Mathematics

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“…The connection weight matrixes of 1 , 2 , 3 , and 4 can be updated according to the gradient descent method, which can be expressed as follows [29,30]:…”

Section: Improved Elman Neuralmentioning

confidence: 99%

A Cooperative Control Method for Fully Mechanized Mining Machines Based on Fuzzy Logic Theory and Neural Networks

Tan

Zhou³

et al. 2014

Advances in Mechanical Engineering

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In a fully mechanized mining face, the coordinated control of coal mining machines has a significant promoting effect to perfect the mining environment and improve the efficiency of coal production and has become a research focus all over the world. In this paper, a cooperative control method based on the integration of fuzzy logic theory and neural networks was proposed. The improved Elman neural network (ENN) through a threshold strategy was presented to predict the running parameters of coal mining machines. On the basis of coupling analysis of coal mining machines, the expert knowledge base of scraper conveyor was established based on fuzzy logic theory. Furthermore, the probabilistic neural network (PNN) was applied to evaluate the running status of scraper conveyor, and the cooperative control flow was designed and analyzed. Finally, a simulation example was provided and the comparison results illustrated that the proposed method was feasible and superior to the manual control.

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“…Narushima and Yabe [33] introduced a new memory gradient method that also uses historical direction information and then derived the global convergence of the method under appropriate conditions. Other methods that use historical iterative information at the current step to improve the algorithmic performance have been reported in [34][35][36][37]. In summary, it would be a good choice to design new algorithms based on historical iterative information in scalar optimization.…”

Section: Introductionmentioning

confidence: 99%

Memory gradient method for multiobjective optimization

Chen¹,

Yang²,

Zhao³

2022

Preprint

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In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the current descent direction and past multi-step iterative information as a new search direction and to obtain a stepsize by virtue of two types of strategies. It is proved that the developed direction with suitable parameters always satisfies the sufficient descent condition at each iteration. Based on mild assumptions, we obtain the global convergence and the rates of convergence for our method. Computational experiments are given to demonstrate the effectiveness of the proposed method.

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A nonmonotone supermemory gradient algorithm for unconstrained optimization

Cited by 7 publications

References 40 publications

A memory gradient method for non-smooth convex optimization

A memory gradient method for non-smooth convex optimization

A Cooperative Control Method for Fully Mechanized Mining Machines Based on Fuzzy Logic Theory and Neural Networks

Memory gradient method for multiobjective optimization

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