Expected residual minimization method for uncertain variational inequality problems

Li, Cunlin; Jia, Zhifu; Zhang, Lin

doi:10.22436/jnsa.010.11.33

Cited by 4 publications

(9 citation statements)

References 11 publications

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“…Based on the discussion of the previous section, we proposed a method of convex combined expectations of the least absolute deviation and least squares about the so-called regularized gap function for nonlinear uncertain variational inequality problems (for short, UNVIP). We succeeded in establishing the UWERM model and extend the results given in [14] to the case where the uncertain event space is compact. As shown in the paper, convergence of global optimal solutions and convergence of stationary points are analyzed respectively.…”

Section: Discussionmentioning

confidence: 79%

“…From Theorem 4.2 of [14] and the continuity of (F, ∇ x F), θ is continuously differentiable over S and…”

Section: Other Preliminariesmentioning

confidence: 99%

“…Let the function F be affine. Some assumptions such as the positive definiteness and the square integrability are given, see [14] for details. To prove the latter theorem, we suppose that the uncertain distribution function Φ(t) is continuous on t ∈ T, and that a third order derivative of the function F exists (denoted by F xtx ).…”

Section: Uwerm Establishment and Hypothesismentioning

confidence: 99%

“…They solve the expected value model based on uncertainty theory. Li and Jia [14] introduced the uncertain variable in the VIP model, they established an expected residual model about the uncertain variable through a regularized gap function. It is given as…”

Section: Introductionmentioning

confidence: 99%

“…x T Gx for x ∈ R n . In [14], Li and Jia considered a linear uncertain variational inequality problem. The properties and convergence analysis of the ERM problem were discussed.…”

Section: Introductionmentioning

confidence: 99%

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Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Postolache

Jia

2019

Mathematics

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A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.

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Section: Discussionmentioning

confidence: 79%

“…From Theorem 4.2 of [14] and the continuity of (F, ∇ x F), θ is continuously differentiable over S and…”

Section: Other Preliminariesmentioning

confidence: 99%

Section: Uwerm Establishment and Hypothesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…x T Gx for x ∈ R n . In [14], Li and Jia considered a linear uncertain variational inequality problem. The properties and convergence analysis of the ERM problem were discussed.…”

Section: Introductionmentioning

confidence: 99%

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Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Postolache

Jia

2019

Mathematics

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Convergence Rate Analysis of a Class of Uncertain Variational Inequalities

Zhao

Yee

2023

IEEE Access

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Variational inequalities theory is a potent tool that can be employed to tackle diverse optimization problems, with applications spanning physics, economics, finance and beyond. Solving the uncertain variational inequalities (UVI) has emerged as a prominent research topic in academia. However, conventional regularization methods for solving UVI are subject to certain limitations on the convergence rate of the algorithm. To overcome this challenge, we opt a class of regularized gap functions which is lower semi-continuous and φ-bounded true convex properties. We establish an expected value equivalent optimization model and demonstrate that the exponential convergence of the regularized gap function. Furthermore, we investigate the subdifferential of the lower semi-continuous and φ-bounded true convex functions (LSTCOS) and develop a deviation between the LSTCOS and its closed convex hull. By utilizing their deviations, we transform the convergence rate of the UVI solution to the uniform exponential convergence of LSTCOS. Finally, we prove that the UVI solution uniformly converges at an exponential rate based on the generalized equation.INDEX TERMS Uncertain variational inequality, φ-bounded true convex function, exponential convergence.

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An Approximation Method for Variational Inequality with Uncertain Variables

Zhang

Yuan

et al. 2023

Advances in Mathematical Physics

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In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.

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Expected residual minimization method for uncertain variational inequality problems

Cited by 4 publications

References 11 publications

Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Convergence Rate Analysis of a Class of Uncertain Variational Inequalities

An Approximation Method for Variational Inequality with Uncertain Variables

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