Comparison of Convergence of the Modified and Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities under Different Conditions

Xu, Haiwen; Zhang, Qianchuan

doi:10.1109/cso.2010.50

Cited by 3 publications

(10 citation statements)

References 12 publications

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“…First, we prove a strong convergence of the MRHSD method under different and suitable restrictions imposed on the parameters (Condition 3.2). The proof of strong convergence is different from the previous proof [20]. Second, based on the approximate projection contraction method, we design an efficient implementation of the MRHSD method for a type of variational inequality problem.…”

Section: It Is Known That Xmentioning

confidence: 90%

“…In Section 4, we design an efficient and implementable nonexpansive mapping T for a type of variational problem based on the approximate projection contraction method. We then review the conditions and theorem presented by Xu et al [20].…”

Section: Convergence Theoremmentioning

confidence: 99%

“…Before analysis and proof, we first review the MRHSD method and related results [20]. Algorithm [20] Take three fixed numbers t, r, g (0, 2h/ 2 ), and let…”

Section: Convergence Theoremmentioning

confidence: 99%

“…However, choosing an efficient and implementable nonexpansive mapping T is a difficult problem, and previous studies did not design numerical experiments or describe an efficient and implementable nonexpansive mapping T [8][9][10][11]19,20]. In Section 4, we design an efficient and implementable nonexpansive mapping T for a type of variational problem based on the approximate projection contraction method.…”

Section: Convergence Theoremmentioning

confidence: 99%

“…Ding et al provided a three-step relaxed hybrid steepest-descent method for variational inequalities [11] and Yao et al [19] provided a simple proof of the method under different conditions. Our group has described a modified and relaxed hybrid steepest descent (MRHSD) method that makes greater use of historical information and minimizes information loss [20].…”

Section: It Is Known That Xmentioning

confidence: 99%

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Efficient implementation of a modified and relaxed hybrid steepest-descent method for a type of variational inequality

2012

J Inequal Appl

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To reduce the difficulty and complexity in computing the projection from a real Hilbert space onto a nonempty closed convex subset, researchers have provided a hybrid steepest-descent method for solving VI(F, K) and a subsequent three-step relaxed version of this method. In a previous study, the latter was used to develop a modified and relaxed hybrid steepest-descent (MRHSD) method. However, choosing an efficient and implementable nonexpansive mapping is still a difficult problem. We first establish the strong convergence of the MRHSD method for variational inequalities under different conditions that simplify the proof, which differs from previous studies. Second, we design an efficient implementation of the MRHSD method for a type of variational inequality problem based on the approximate projection contraction method. Finally, we design a set of practical numerical experiments. The results demonstrate that this is an efficient implementation of the MRHSD method.

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Section: It Is Known That Xmentioning

confidence: 90%

Section: Convergence Theoremmentioning

confidence: 99%

“…Before analysis and proof, we first review the MRHSD method and related results [20]. Algorithm [20] Take three fixed numbers t, r, g (0, 2h/ 2 ), and let…”

Section: Convergence Theoremmentioning

confidence: 99%

Section: Convergence Theoremmentioning

confidence: 99%

Section: It Is Known That Xmentioning

confidence: 99%

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Efficient implementation of a modified and relaxed hybrid steepest-descent method for a type of variational inequality

2012

J Inequal Appl

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The partial solutions consideration based self-adaptive evolutionary algorithm: A learning structure of neuro-fuzzy networks

Hung¹,

Lin²

2012

Expert Systems with Applications

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An Improved Vector Control Strategy for Switched Reluctance Motor Drive Based on the Two-Degree-of-Freedom Internal Model Control

et al. 2022

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The unipolar sinusoidal current excited control strategy of the switched reluctance motor (SRM) has been widely attended for its wide driving area and acceptable torque ripple. However, due to the SRM’s time-varying, non-linear, and high coupling features, the traditional vector control strategies are unable to provide excellent current control performance. In this paper, a novel vector control method based on a two-degree-of-freedom internal model control (2DOF IMC) is proposed. The main objectives of this article are to improve the control precision and to enhance the system’s robustness. Firstly, considering the non-linear characteristics of the system in the rotating reference frame, a 2DOF IMC controller based on a simplified SRM model is designed and the stability analysis of the controller is implemented. Since the time-varying disturbance cannot be effectively eliminated using the 2DOF IMC with constant filter parameters, a simple adaptive disturbance observer (ADO) is incorporated into the inner-loop system to online estimate and eliminate these disturbances. Moreover, a stability analysis based on Lyapunov theory is also presented, and the ADO’s stability and convergence are guaranteed by tuning the adaption gain law. Finally, the effectiveness of the proposed control strategy is demonstrated by experiments, and the results illustrate that the proposed method can effectively improve the control and disturbance rejection performance of the SRM drives.

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Comparison of Convergence of the Modified and Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities under Different Conditions

Cited by 3 publications

References 12 publications

Efficient implementation of a modified and relaxed hybrid steepest-descent method for a type of variational inequality

Efficient implementation of a modified and relaxed hybrid steepest-descent method for a type of variational inequality

The partial solutions consideration based self-adaptive evolutionary algorithm: A learning structure of neuro-fuzzy networks

An Improved Vector Control Strategy for Switched Reluctance Motor Drive Based on the Two-Degree-of-Freedom Internal Model Control

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