The Forward–Backward Algorithm and the Normal Problem

Walaa M. Moursi ()
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Walaa M. Moursi: Stanford University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 3, No 5, 605-624

Abstract: Abstract The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward–backward operator. We also provide a formula for the range of the displacement map of the forward–backward operator. Several examples illustrate our theory.

Keywords: Attouch–Théra duality; Firmly nonexpansive mapping; Fixed point; Forward–backward splitting operator; Normal problem; Primary 47H09; 49M27; 65K05; 65K10; Secondary 47H05; 47H14; 49M29; 49N15 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1113-4

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