Extrapolated cyclic subgradient projection methods for the convex feasibility problems and their numerical behaviour

Cegielski, Andrzej; Nimana, Nimit

doi:10.1080/02331934.2018.1509214

Cited by 10 publications

(12 citation statements)

References 18 publications

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“…where the fifth inequality holds from the assumption that {β n } ∞ n=1 ⊂ (0, 1] and the boundedness of the sequences {x n } ∞ n=1 and {u n } ∞ n=1 . Invoking the obtained inequality (10) in (6), we obtain…”

Section: Lemma 16mentioning

confidence: 98%

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A Sequential Constraint Method for Solving Variational Inequality over the Intersection of Fixed Point Sets

Prangprakhon,

Nimana,

Petrot

2020

Preprint

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Section: Lemma 16mentioning

confidence: 98%

“…Fix T i and n ≥ 1 be fixed. By utilizing the inequalities ( 7), (10), and Proposition 1, we note that…”

Section: Lemma 18mentioning

confidence: 99%

A Sequential Constraint Method for Solving Variational Inequality over the Intersection of Fixed Point Sets

Prangprakhon,

Nimana,

Petrot

2020

Preprint

Self Cite

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“…(Theorem 2.1.50, [8]). In 2018, Cegielski and Nimana [26] proposed the following extrapolated operator,…”

Section: Convex Minimization With Nonsmooth Functional Constraintsmentioning

confidence: 99%

“…where U i := P i P i−1 ...P 1 for i = 1, 2, ..., m and U 0 := I. Note that the operator P λ,σ is SQNE with Fix P λ,σ = Fix P = ∅ ( [26], Theorem 3.2). By means of T := P λ,σ or T := P, the problem (15) is nothing else than Problem 1 and Algorithm 1 is applicable for the problem (15).…”

Section: Convex Minimization With Nonsmooth Functional Constraintsmentioning

confidence: 99%

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Nimana

2020

Symmetry

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In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

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“…, m, satisfy the demi-closedness principle. Along the line of [7], Cegielski and Nimana [8] indicated that there are some practical situations in which the value of the extrapolation function σ can be enormously large, which consequently may produce some uncertainties in numerical experiments. In order to avoid these situations, they proposed an algorithm called the modified extrapolated cyclic subgradient projection method (MECSPM).…”

Section: Introductionmentioning

confidence: 99%

Extrapolated Sequential Constraint Method for Variational Inequality over the Intersection of Fixed-Point Sets

Prangprakhon¹,

Nimana²

2020

Preprint

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This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each iteration, the proposed method is updated based on the ideas of a hybrid conjugate gradient method used to accelerate the well-known hybrid steepest descent method, and an extrapolated cyclic cutter method for solving a common fixed point problem. We prove strong convergence of the method under some suitable assumptions of step-size sequences. We finally show the numerical efficiency of the proposed method compared to some existing methods.

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Extrapolated cyclic subgradient projection methods for the convex feasibility problems and their numerical behaviour

Cited by 10 publications

References 18 publications

A Sequential Constraint Method for Solving Variational Inequality over the Intersection of Fixed Point Sets

A Sequential Constraint Method for Solving Variational Inequality over the Intersection of Fixed Point Sets

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Extrapolated Sequential Constraint Method for Variational Inequality over the Intersection of Fixed-Point Sets

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