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Convergence analysis of a generalized proximal algorithm for multiobjective quasiconvex minimization on Hadamard manifolds.
- Source :
-
Optimization . Sep2024, Vol. 73 Issue 9, p2819-2844. 26p. - Publication Year :
- 2024
-
Abstract
- In this paper, we introduce a generalized inexact scalarized proximal point algorithm to find Pareto-Clarke critical points and Pareto efficient solutions of quasiconvex multivalued functions defined on Hadamard manifolds considering vectorial and scalar errors to find a critical point of the regularized proximal function in each iteration. Under some assumptions on the problem, we obtain the global convergence of the sequence to a Pareto-Clarke critical point and assuming an extra condition on the proximal parameters we establish convergence to a Pareto efficient solution, approximately linear/superlinear rate of convergence and finite termination of the algorithm. In the convex case, we prove the convergence to a Pareto efficient solution point (more than a weak Pareto efficient solution point). The results of the paper are new even in the Euclidean space. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 73
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 179170140
- Full Text :
- https://doi.org/10.1080/02331934.2023.2234939