Active‐Set Newton Methods and Partial Smoothness

Adrian S. Lewis () and Calvin Wylie
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Adrian S. Lewis: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
Calvin Wylie: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853

Mathematics of Operations Research, 2021, vol. 46, issue 2, 712-725

Abstract: Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

Keywords: 90C31; 49M05; 65K10; Primary: programming: nondifferentiable; secondary: mathematics: systems solution; partial smoothness; active set identification; variational inequality (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:2:p:712-725

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