A proximal-gradient inertial algorithm with Tikhonov regularization: strong convergence to the minimal norm solution
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 par...
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| Vydáno v: | Optimization methods & software Ročník 40; číslo 4; s. 947 - 976 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Taylor & Francis
04.07.2025
|
| Témata: | |
| ISSN: | 1055-6788, 1029-4937 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
|---|---|
| ISSN: | 1055-6788 1029-4937 |
| DOI: | 10.1080/10556788.2025.2517172 |