Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties

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Convex Analysis And Nonlinear Optimization (2000, unknown): “∗∗ (Conical open mapping [8]) Define two closed convex cones in R(3): Q = {(x, y, z) ∈ R(3) | y(2) ≤ 2xz, x, z ≥ 0}.”
A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix (2006, background): “We refer the reader to [2, 3, 5, 6, 10, 15, 36, 37] for related developments.”
Strong CHIP, normality, and linear regularity of convex sets (2005, background): “If dimH ≤ 3, it was proved that (1) ⇔ (2) (see [1]) and (2) ⇔ (3) (see [10]).”
A simple closure condition for the normal cone intersection formula (2004, background): “If the interior-point condition that (intD) ∩ C = ∅ (or its recent generalization that the cone generated by (C −D), cone(C −D), is a closed subspace [13, 15, 10]) is satisfied or the bounded linear regularity condition [4, 5], when X is a Euclidean space, is satisfied, then the normal cone intersec”