New Farkas-type constraint qualifications in convex infinite programming

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ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints (2009, background): “Ref. [ 13 ], that x is an optimal solution to (P) if and only if there exists λ ∈ R (T ) + such that the optimality condition (5) is satisfied.”
Optimality conditions for non-smooth semi-infinite programming (2010, methodology): “Also, in 3 , 5 and 12 the authors deal with convex SIP involving lower semicontinuous proper functions (the decision space is not necessarily ℝ n ), and they are focused on BCQ and the so-called cone constraint CQ, using the convex subdifferential and the epigraphs on conjugate functions as”
A closedness condition and its applications to DC programs with convex constraints (2010, methodology): “Note that such a problem can be reduced to the model (Q) by letting h : R!R with h(x)1⁄4 (hi(x))i2 I and S 1⁄4 RIþ [13,14].”
Constraint qualifications for optimality conditions and total Lagrange dualities in convex infinite programming (2010, background): “Following [2], the characteristic cone K of (3.”