An alternative formulation for a new closed cone constraint qualification

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A closedness condition and its applications to DC programs with convex constraints (2010, methodology): “In particular, it was shown that the constraint qualification (FM) is strictly weaker than several generalized Slater type ones, and weaker than the Robinson type one stating that R+[S + h(C)] is a closed subspace (see [9, 23] for more details).”
A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces (2008, unknown): “Radu Ioan Boţ∗1, Sorin-Mihai Grad ∗∗1, and Gert Wanka∗∗∗1”
Constraint qualifications for optimality conditions and total Lagrange dualities in convex infinite programming (2010, background): “1) has been studied in [13,14], and also studied in [12,15,17,19,21,22,39,40] for the special case when X, Y are Banach spaces (or normed spaces), and g : X → Y is S-convex and continuous.”
Constraint Qualifications Characterizing Lagrangian Duality in Convex Optimization (2008, background): “For instance, if Y is a finite dimensional space and if 0 ∈ ri(g(C) + S) then (CQ1) holds, where for a set E ⊂ Y , the relative interior of E is denoted by ri(E). For details, see [11, 16 , 17].”