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Projective Splitting with Forward Steps only Requires Continuity

Patrick R. Johnstone(patrick.r.johnstone***at***gmail.com)
Jonathan Eckstein(jeckstei***at***business.rutgers.edu )

Abstract: A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward steps are performed in finite-dimensional spaces: a backtracking linesearch yields a convergent algorithm for operators that are merely continuous with full domain.


Category 1: Convex and Nonsmooth Optimization

Category 2: Complementarity and Variational Inequalities


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Entry Submitted: 09/17/2018
Entry Accepted: 09/17/2018
Entry Last Modified: 09/17/2018

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