Geodesic
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
Archivum mathematicum, Tome 55 (2019) no. 3, pp. 167-194

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In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $\delta $-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition $\sum _{n=1}^\infty \beta _n\Vert x_{n-1} -x_n\Vert + \infty $ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature.
DOI : 10.5817/AM2019-3-167
Classification : 46N10, 47H10, 47J25, 65K10, 65K15
Keywords: proximal gradient algorithm; proximal operator; demimetric mappings; inertial algorithm; viscosity approximation; Meir Keeler contraction; fixed point theory 
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Jolaoso, L.O.; Abass, H.A.; Mewomo, O.T. A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space. Archivum mathematicum, Tome 55 (2019) no. 3, pp. 167-194. doi: 10.5817/AM2019-3-167

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