Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Aremu, Kazeem Olalekan; Izuchukwu, Chinedu; Ogwo, Grace Nnenanya

doi:10.3934/jimo.2020063

Cited by 30 publications

(12 citation statements)

References 40 publications

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“…The solution set of the Problem (57) is denoted by arg min x∈C φ(x). For details on CMP and related optimization problems, see [1,6,7,22,21,39]. By applying Theorem 3.4 and Lemma 4.1, we obtain the following result.…”

Section: Applicationmentioning

confidence: 86%

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

Owolabi¹,

Alakoya²,

Taiwo³

et al. 2022

NACO

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In this paper, we present a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces. Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space. The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence. Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm.

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Section: Applicationmentioning

confidence: 86%

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

Owolabi¹,

Alakoya²,

Taiwo³

et al. 2022

NACO

Self Cite

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“…MPs play vital role in nonlinear analysis and geometry. They have notable applications in computer vision, machine learning, electronic structure computation, system balancing and robot manipulation, and several iterative algorithms have been studied for solving MPs and related optimization problems (see [1,4,5,19,20,22,23,24,25,26,34,33,36,42,43,44,48] and references therein). The Proximal Point Algorithm (PPA) is one of the most popular and effective methods for solving MPs.…”

Section: Minimization and Fixed Point Problems For Non-self Mappings 307mentioning

confidence: 99%

A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces

Aremu¹,

Izuchukwu²,

Oyewole³

2021

Revista De La Unión Matemática Argentina

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We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mapping and the resolvent of a convex function in a Hadamard space. We obtain a strong convergence of the proposed algorithm to a minimizer of a convex function which is also a fixed point of a Lipschitz hemicontractive non-self mapping. Furthermore, we give a numerical example to illustrate and support our method. Our proposed method improves and extends some recent works in the literature.

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“…If ∇h 1 is Lipschitz continuous with a coefficient L > 0 and α ∈ (0, 2/L), then the forward-backward operator FB α is nonexpansive. In this case, we can employ fixed point approximation methods for the class of nonexpansive operators to solve (1). One of the popular methods is known as the forward-backward splitting (FBS) algorithm [8,18].…”

Section: Introductionmentioning

confidence: 99%

An accelerated viscosity forward-backward splitting algorithm with the linesearch process for convex minimization problems

2021

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In this paper, we consider and investigate a convex minimization problem of the sum of two convex functions in a Hilbert space. The forward-backward splitting algorithm is one of the popular optimization methods for approximating a minimizer of the function; however, the stepsize of this algorithm depends on the Lipschitz constant of the gradient of the function, which is not an easy work to find in general practice. By using a new modification of the linesearches of Cruz and Nghia [Optim. Methods Softw. 31:1209–1238, 2016] and Kankam et al. [Math. Methods Appl. Sci. 42:1352–1362, 2019] and an inertial technique, we introduce an accelerated viscosity-type algorithm without any Lipschitz continuity assumption on the gradient. A strong convergence result of the proposed algorithm is established under some control conditions. As applications, we apply our algorithm to solving image and signal recovery problems. Numerical experiments show that our method has a higher efficiency than the well-known methods in the literature.

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Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Cited by 30 publications

References 40 publications

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces

An accelerated viscosity forward-backward splitting algorithm with the linesearch process for convex minimization problems

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