A Duality Theorem for Infinite Dimensional Improper Mathematical Programming Problems
Yugoslav journal of operations research, Tome 6 (1996) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A mathematical programming problem is called proper if it is solvable together with its dual and both problems share the same optimal value. Otherwise it is called improper (or contradictory). In a situation of impropriety , standard duality gives only limited information about the problem . In this paper , for improper linear programs in Banach space, a (substantial) duality scheme is suggested and the corresponding duality theorem is proved. 
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     author = {Anatolly Anatolijevich Vatolin},
     title = {A {Duality} {Theorem} for {Infinite} {Dimensional} {Improper} {Mathematical} {Programming} {Problems}},
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Anatolly Anatolijevich Vatolin. A Duality Theorem for Infinite Dimensional Improper Mathematical Programming Problems. Yugoslav journal of operations research, Tome 6 (1996) no. 1. https://geodesic-test.mathdoc.fr/item/YJOR_1996_6_1_a2/