New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems

Farkas-type results for inequality systems with composed convex functions via conjugate duality

“…However, similar results can be obtained using another approach (see [1]), namely considering an equivalent problem to the primal one, but whose dual can be easier established. The equivalent problem is introduced considering an auxiliary variable.…”

“…It can be easily shown that in the general case strong duality between the primal problem and its dual can fail (see [17]). In order to avoid this situation the following constraint qualification is considered ( [1], see also [7])…”

“…As the authors proved in [1], (CQ) is weaker than the constraint qualifications concerning composed convex optimization problems given until now in the literature (see [9,13]). …”

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

“…Other papers deal with a special case of the problem presenting results concerning only the mentioned composition of functions, renouncing the first term of the sum of functions, among which let us mention Lemaire's [10] and our article [2], where we say more about previous works containing optimization problems in which such composed functions appeared. Different to [2], we work here in separated locally convex spaces, considering for functions having their ranges in infinite dimensional spaces a generalized notion of lower-semicontinuity. Precisely, we assume that these functions are K -epi-closed (cf.…”

An Analysis of Some Dual Problems for (0, Q) Invexity-Type Nonlinear Programming Problems

“…In [8,9], Fenchel-Lagrange duality was studied in convex optimization. In [10,11,12], interesting applications for Fenchel-Lagrange duality were given in multiobjective optimization and Farkas results.…”