A new inertial-type hybrid projection-proximal algorithm for monotone inclusions

作者：Mainge Paul Emile^*; Merabet Nora

来源：Applied Mathematics and Computation, 2010, 215(9): 3149-3162.

DOI：10.1016/j.amc.2009.10.026

• Convex minimization
• Maximal monotone operator
• Proximal point algorithm
• Inexact computations
• Inertial extrapolation
• Inexact Newton method

This paper investigates an enhanced proximal algorithm with interesting practical features and convergence properties for solving non-smooth convex minimization problems, or approximating zeroes of maximal monotone operators, in Hilbert spaces. The considered algorithm involves a recent inertial-type extrapolation technique, the use of enlargement of operators and also a recently proposed hybrid strategy, which combines inexact computation of the proximal iteration with a projection. Compared to other existing related methods, the resulting algorithm inherits the good convergence properties of the inertial-type extrapolation and the relaxed projection strategy. It also inherits the relative error tolerance of the hybrid proximal-projection method. As a special result, an update of inexact Newton-proximal method is derived and global convergence results are established.

• 出版日期2010-1-1