Strong convergence result for monotone variational inequalities

Shehu, Yekini; Iyiola, Olaniyi S.

doi:10.1007/s11075-016-0253-1

Cited by 73 publications

(48 citation statements)

References 39 publications

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“…2. In the industrial Example 5.1, Table 1 clearly shows that our proposed algorithm is better (cpu time taken and number of iterations) compared to that of YNE algorithm proposed in [41] for different values of N . 3.…”

Section: : Computementioning

confidence: 91%

“…Observe that, in finding α n , the operator A is evaluated (possibly) many times, but no extra projections onto the set C are needed. This is in contrast to a couple of related algorithms for the solution of monotone variational inequalities where the calculation of a suitable stepsize requires (possibly) many projections onto C, see, e.g., [14,27,41] 4. Convergence analysis.…”

Section: Algorithm 31 Extragradient-type Methodsmentioning

confidence: 99%

“…Many a time, it is difficult to estimate the Lipschitz constant of the given monotone operator A. The usual approaches to overcome this difficulty consist in some prediction of a stepsize with its further correction (see [14,27,35,41,43,45]) or in a usage of an Armijo type linesearch procedure along a feasible direction (see [25,26,42,46]). Usually the latter approach is more effective, since very often the former approach requires too many projections onto the feasible set per iteration and can be very computationally expensive.…”

Section: Yekini Shehu and Olaniyi Iyiolamentioning

confidence: 99%

“…We perform our Algorithm 3.1 using different choices of N = 4, 10, and 20, different initial choices x 1 generated randomly in the interval [1,40] We compare our proposed method with Algorithm 3.1 (YNE Alg.) of [41]:…”

Section: Industrial Example: Electricity Productionmentioning

confidence: 99%

See 3 more Smart Citations

On a modified extragradient method for variational inequality problem with application to industrial electricity production

Shehu¹,

Iyiola²

2019

Journal of Industrial &Amp; Management Optimization

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In this paper, we present a modified extragradient-type method for solving the variational inequality problem involving uniformly continuous pseudomonotone operator. It is shown that under certain mild assumptions, this method is strongly convergent in infinite dimensional real Hilbert spaces. We give some numerical computational experiments which involve a comparison of our proposed method with other existing method in a model on industrial electricity production.

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Section: : Computementioning

confidence: 91%

Section: Algorithm 31 Extragradient-type Methodsmentioning

confidence: 99%

Section: Yekini Shehu and Olaniyi Iyiolamentioning

confidence: 99%

Section: Industrial Example: Electricity Productionmentioning

confidence: 99%

See 2 more Smart Citations

On a modified extragradient method for variational inequality problem with application to industrial electricity production

Shehu¹,

Iyiola²

2019

Journal of Industrial &Amp; Management Optimization

Self Cite

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“…Very recently, solving the VIP (5) when A is a Lipschitz continuous monotone mapping such that the Lipschitz constant is unknown in Hilbert spaces by using the following viscosity-type subgradient extragradient-like method was proposed by Shehu and Iyiola [19].…”

Section: Pseudo-monotone Ifmentioning

confidence: 99%

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

et al. 2020

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In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

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Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

Godwin

Izuchukwu

2022

Math Methods in App Sciences

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In this article, we propose a new efficient self‐adaptive method and prove that it converges strongly to a minimum‐norm solution of a generalized split feasibility problem in real Hilbert spaces. The proposed method is derived from a definite discrete dynamical system in time, which combines both the relaxation and inertial techniques for the purpose of increasing the rate of convergence of the iterative scheme. Furthermore, the method requires the monotonicity and Lipschitz continuity condition of the underlying single‐valued cost operator A$$ A $$, and it employs some simple self‐adaptive stepsizes that are generated at each iteration by some easy computations. As a by‐product, we obtain methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Two major merits of our scheme in solving image restoration problems over related schemes are the higher signal‐to‐noise ratio value and lower CPU time for generating recovered images. Finally, we analyze our methods with different related strong convergent methods in the literature.

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Strong convergence result for monotone variational inequalities

Cited by 73 publications

References 39 publications

On a modified extragradient method for variational inequality problem with application to industrial electricity production

On a modified extragradient method for variational inequality problem with application to industrial electricity production

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

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