Generalized forward–backward splitting with penalization for monotone inclusion problems

Nimit Nimana () and Narin Petrot ()
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Nimit Nimana: Khon Kaen University
Narin Petrot: Naresuan University

Journal of Global Optimization, 2019, vol. 73, issue 4, No 7, 825-847

Abstract: Abstract We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.

Keywords: Monotone operator; Monotone inclusion; Hierarchical optimization; Forward–backward algorithm; 47H05; 65K05; 65K10; 90C25 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-018-00730-5

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