Abstract
We present some total Lagrange duality results for inequality systems involving infinitely many DC functions. By using properties of the subdifferentials of involved functions, we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the stable total Lagrange duality to hold.
Highlights
Let X be a real locally convex Hausdorff topological vector space, whose dual space X∗ is endowed with the weak∗ topologies W ∗(X∗, X)
H(x) + λtht(x) where R(+T) is the cone consisting of vector ∈ RT with nonnegative and only finitely many nonzero coordinates, that is, R(+T) = ∈ RT : λt ≥ for each t ∈ T and only finitely many λ =
Several sufficient and/or necessary conditions were given in the past in order to eliminate the above-mentioned duality gap, see, for example, [, ] and the references therein
Summary
Let X be a real locally convex Hausdorff topological vector space, whose dual space X∗ is endowed with the weak∗ topologies W ∗(X∗, X). Following [ ], we define the Lagrange function L : H∗ ×R(+T) → R for the DC optimization problem For the problem of total Lagrange duality, one seeks conditions ensuring that the following implication holds for x ∈ dom(f – g) ∩ A: f
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
