On the Relations Between Different Dual Problems in Convex Mathematical Programming

Farkas-type Results for Max-functions and Applications

“…This approach bases on the theory of conjugate duality for convex optimization problems, namely by using the so-called Fenchel and Fenchel-Lagrange duality concepts (see also [1], [2], [10], [12]). Moreover the authors show how these new Farkas-type results generalize some of the results obtained by Jeyakumar in [7].…”

Conjugate dual problems in constrained set-valued optimization and applications

“…In [16] (see also [5]), the relation supðP Ã 1 Þ P supðP Ã 3 Þ has been proved. Clearly, Corollary 4.1(ii) shows the case.…”

“…We mention that the Fenchel-Lagrange dual problem for scalar-valued case is due to Wanka and Bot ß [16].…”

“…Let X ¼ R n , Y ¼ R and Z ¼ R k . Then the dual problems ðD L Þ and ðD FL Þ reduce to the following dual problems ðP Ã 1 Þ and ðP Ã 3 Þ which have been constructed in [16], respectively…”

A Duality Approach for a Class of Semivectorial Bilevel Programming Problems

“…In this paper, we will extend this duality approach via scalarization to the vectorial case where the corresponding upper level is vectorial and the lower level is non parameterized and scalar. The duality that we consider is the so-called Fenchel-Lagrange duality (see [12]). We note that in order to establish strong duality, we will need the Slater constraint qualification.…”