A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings

Arfat, Yasir; Khan, Muhammad Aqeel Ahmad; Cho, Yeol Je

doi:10.37193/cjm.2023.01.21

CJM

2022

DOI: 10.37193/cjm.2023.01.21

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A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings

Yasir Arfat¹,

Muhammad Aqeel Ahmad Khan²,

Yeol Je Cho³

Abstract: In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications.

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Cited by 3 publications

References 18 publications

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Some variants of the hybrid extragradient algorithm in Hilbert spaces

Arfat,

Kumam,

Khan

et al. 2024

J Inequal Appl

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This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of $\Bbbk $ k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications.

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Some variants of the hybrid extragradient algorithm in Hilbert spaces

Arfat,

Kumam,

Khan

et al. 2024

J Inequal Appl

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show abstract

Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems

Arfat,

Phiangsungnoen,

Kumam

et al. 2023

MATH

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<abstract><p>In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of $ \eta $-demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of control conditions. We also provide a numerical example to demonstrate the applicability of the variant with some applications.</p></abstract>

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An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

Arfat

Phiangsungnoen

Khan

et al. 2023

MATH

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<abstract><p>In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of $ \Bbbk $-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. Theoretical results comprise strong convergence characteristics under suitable sets of constraints as well as numerical results are established for the underlying algorithm. Applications to signal processing as well as various abstract problems are also incorporated.</p></abstract>

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A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings

Cited by 3 publications

References 18 publications

Some variants of the hybrid extragradient algorithm in Hilbert spaces

Some variants of the hybrid extragradient algorithm in Hilbert spaces

Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems

An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

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