Isotonicity of the projection onto the monotone cone

2012/01/23 by A. B. Németh, Németh, A. B., S. Z. Németh +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #Optimization and Variational Analysis #math.OC

paper · pdf · doi:10.48550/arxiv.1201.4677

arxiv created 2012/01/23 · arxiv updated 2012/01/24

Abstract

A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges admitting isotone metric projection with respect to the semi-order induced by them are characterized. The obtained result is used to show that the monotone wedge (called monotone cone in regression theory) admits isotone projection.

Related

• Isotonic regression and isotonic projection
• Order isotonicity of the metric projection onto a closed convex cone
• Lattice-like operations and isotone projection sets
• Semi-monotone sets
• How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms