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A proximal-gradient inertial algorithm with Tikhonov regularization: strong convergence to the minimal norm solution.

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Titel: A proximal-gradient inertial algorithm with Tikhonov regularization: strong convergence to the minimal norm solution.
Autoren: László, Szilárd Csaba1 (AUTHOR) szilard.laszlo@math.utcluj.ro
Quelle: Optimization Methods & Software. Aug2025, Vol. 40 Issue 4, p947-976. 30p.
Schlagwörter: *TIKHONOV regularization, *CONVEX programming, *COST functions, *SUBGRADIENT methods, *OPTIMIZATION algorithms
Abstract: We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection with the minimization problem of the sum of a convex lower semi-continuous function f and a smooth convex function g. For the appropriate setting of the parameters, we provide the strong convergence of the generated sequence $ (x_k){_{k\ge 0}} $ (x k) k ≥ 0 to the minimum norm minimizer of our objective function f + g. Further, we obtain fast convergence to zero of the objective function values in a generated sequence but also for the discrete velocity and the sub-gradient of the objective function. We also show that for another setting of the parameters the optimal rate of order $ \mathcal {O}(k^{-2}) $ O (k − 2) for the potential energy $ (f+g)(x_k)-\min (f+g) $ (f + g) (x k) − min (f + g) can be obtained. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection with the minimization problem of the sum of a convex lower semi-continuous function f and a smooth convex function g. For the appropriate setting of the parameters, we provide the strong convergence of the generated sequence $ (x_k){_{k\ge 0}} $ (x k) k ≥ 0 to the minimum norm minimizer of our objective function f + g. Further, we obtain fast convergence to zero of the objective function values in a generated sequence but also for the discrete velocity and the sub-gradient of the objective function. We also show that for another setting of the parameters the optimal rate of order $ \mathcal {O}(k^{-2}) $ O (k − 2) for the potential energy $ (f+g)(x_k)-\min (f+g) $ (f + g) (x k) − min (f + g) can be obtained. [ABSTRACT FROM AUTHOR]
ISSN:10556788
DOI:10.1080/10556788.2025.2517172