An extrapolated fixed-point optimization method for strongly convex smooth optimizations

Duangdaw Rakjarungkiat; Nimit Nimana; Duangdaw Rakjarungkiat; Nimit Nimana

doi:10.3934/math.2024210

AIMS Mathematics

2024, Volume 9, Issue 2: 4259-4280. doi: 10.3934/math.2024210

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Research article

An extrapolated fixed-point optimization method for strongly convex smooth optimizations

Duangdaw Rakjarungkiat ,
Nimit Nimana ^,

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 21 November 2023 Revised: 21 December 2023 Accepted: 05 January 2024 Published: 16 January 2024
MSC : 47H09, 47J05, 65K10, 90C25

In this work, we focused on minimizing a strongly convex smooth function over the common fixed-point constraints. We proposed an extrapolated fixed-point optimization method, which is a modified version of the extrapolated sequential constraint method with conjugate gradient direction. We proved the convergence of the generated sequence to the unique solution to the considered problem without boundedness assumption. We also investigated some numerical experiments to underline the effectiveness and performance of the proposed method.
- conjugate gradient method,
- cutter,
- extrapolated method,
- strong convergence,
- strong convexity
Citation: Duangdaw Rakjarungkiat, Nimit Nimana. An extrapolated fixed-point optimization method for strongly convex smooth optimizations[J]. AIMS Mathematics, 2024, 9(2): 4259-4280. doi: 10.3934/math.2024210

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Abstract

In this work, we focused on minimizing a strongly convex smooth function over the common fixed-point constraints. We proposed an extrapolated fixed-point optimization method, which is a modified version of the extrapolated sequential constraint method with conjugate gradient direction. We proved the convergence of the generated sequence to the unique solution to the considered problem without boundedness assumption. We also investigated some numerical experiments to underline the effectiveness and performance of the proposed method.

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