Extragradient methods for differential variational inequality problems and linear complementarity systems

Fatemi, S. Z.; Shamsi, M.; Bozorgnia, Farid

doi:10.1002/mma.4523

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…For converting (7) to classical form of VI, note that the following matrix is nonsingular (theorem 3.6.11 of Stoer and Bulirsch 12 and distinctly of j ):…”

Section: Theorem 1 Problem 6 Can Be Reformulated As a VImentioning

confidence: 99%

“…Since the matrix Q defined in (8) is nonsingular, then the matrix Λ defined in (9) is also nonsingular; so = Λ −1 ′ . Now, by substituting = Λ −1 ′ in (7), the following equivalent VI to (7) is obtained:…”

Section: Theorem 1 Problem 6 Can Be Reformulated As a VImentioning

confidence: 99%

“…Furthermore, Friesz considered a special category of DVI problems that could become a VI in Hilbert space, and he suggested some methods based on solving the corresponding VI in Hilbert space, such as the gap functions and fixed‐point methods . Then, Fatemi et al, provided some extragradient methods for solving DVIs, in order to modify the convergence conditions of the fixed‐point method.…”

Section: Introductionmentioning

confidence: 99%

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Collocation method for differential variational inequality problems

Fatemi

Shamsi

Razmjooy

2018

Int J Numerical Modelling

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In this paper, a Jacobi collocation method is presented for solving differential variational inequalities (DVIs). Differential variational inequalities consist of a differential equation and a variational inequality. A type of Jacobi-Gauss collocation scheme with N knots is applied to the differential part of the problem whereas another type of Jacobi-Gauss collocation scheme with N + 1 knots is applied to the variational part of it. So the DVI problem turns into a variational inequality problem. Electrical circuits with nonsmooth elements like ideal diodes are an important class of physical systems, which can be modeled as DVI problems. So in the numerical experiments, 1 example with smooth solutions and 4 illustrative examples of simple electrical circuits with ideal diodes are considered. Numerical results demonstrate the effectiveness of the proposed method but slow convergence for the proposed method for some examples. The reason for slow convergence in this method is that the solutions of these DVIs are nonsmooth. KEYWORDS collocation method, differential variational inequality, variational inequality Int J Numer Model. 2019;32:e2466.wileyonlinelibrary.com/journal/jnm

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“…For converting (7) to classical form of VI, note that the following matrix is nonsingular (theorem 3.6.11 of Stoer and Bulirsch 12 and distinctly of j ):…”

Section: Theorem 1 Problem 6 Can Be Reformulated As a VImentioning

confidence: 99%

Section: Theorem 1 Problem 6 Can Be Reformulated As a VImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collocation method for differential variational inequality problems

Fatemi

Shamsi

Razmjooy

2018

Int J Numerical Modelling

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“…For this purpose, volatility, dividend, interest rate, and installment rate, which are assumed constant in the classical Black–Scholes model, are allowed to take diverse values by switching states governed by the Markov process. For the pricing installment option under this model, we write the obtained problem as a linear complementarity problem 22 and proposed a finite element method in order to solve the truncated problem. We examine the accuracy of the numerical method with some numerical results.…”

Section: Introductionmentioning

confidence: 99%

Numerical approach for coupled systems resulting from pricing of derivatives: Modeling and pricing of installment options

Heidari

2022

Math Methods in App Sciences

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In this paper, we proposed Markov‐modulated models to value vanilla European‐style continuous‐installment options with a numerical approach. The flexibility in installment options to paying installments or stopping payments makes these options more attractive to holders. We consider regime‐switching models for the dynamic of the underlying asset; in this way, the pricing problem of installment options can be formulated as coupled partial differential equations with free boundary features, which in many ways is similar to the free boundary problem for vanilla American options due to the possibility of early exercise. To value the installment options in this model, we express the problem as a linear complementarity problem (LCP), then we apply a finite element method as the numerical solving procedure to the resulting variational inequality. We illustrate some numerical results to examine the suitability of the proposed model and the accuracy of the applied numerical method for the pricing problem of installment options.

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“…The theory of variational inequality has been investigated extensively as methodology to study of equilibrium problems. Equilibrium is a central concept in numerous disciplines including economics, management science, operations research, and engineering, see [5,8,11].…”

Section: Introductionmentioning

confidence: 99%

Existence Result for Generalized Variational Equality

Shafie,

Bozorgnia

2018

Preprint

Self Cite

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In this paper we prove the existence of solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some sufficient conditions that under them the generalized equation 0 ∈ T (x) has a solution. Furthermore, by using generalized results of continuity and monotonicity, we extend the related existence results and we answer an open problem proposed by Kassay and Miholka (J Optim Theory Appl 159 (2013) 721-740).

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Extragradient methods for differential variational inequality problems and linear complementarity systems

Cited by 3 publications

References 26 publications

Collocation method for differential variational inequality problems

Collocation method for differential variational inequality problems

Numerical approach for coupled systems resulting from pricing of derivatives: Modeling and pricing of installment options

Existence Result for Generalized Variational Equality

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