An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator

Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2021 Số 1 - 2021
Minh N. Dao1, Hung M. Phan2
1School of Engineering, Information Technology and Physical Sciences, Federation University Australia, Ballarat, Australia
2Department of Mathematical Sciences, Kennedy College of Sciences, University of Massachusetts Lowell, Lowell, USA

Tóm tắt

AbstractSplitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem.

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Fixed Point Theory and Algorithms for Sciences and Engineering

Tập 2021 Số 1

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