A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an in...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2024; no. 1; pp. 124 - 23
Main Authors: Xue, Zhonghui, Ma, Qianfeng
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 20.09.2024
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Analysis
Applications of Mathematics
Approximation
Dependent variables
Independent variables
Kurdyka–Łojasiewicz property
Linear operators
Mathematics
Mathematics and Statistics
Nonconvex-nonsmooth optimization
Optimization
Parameter modification
Proximal minimization algorithm
Weak inertial
49K99
Kurdyka–Łojasiewicz property
49J53
Nonconvex-nonsmooth optimization
Weak inertial
Proximal minimization algorithm
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03206-1