 On the subdifferential of the value function in economic optimization problemsJean-Marc Bonnisseau and Cuong Le van Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL Abstract: The purpose of this paper is to provide a unified treatment to find sufficient conditions for the existence of a subgradient of the value function associated with a convex optimization problem. We recall basic results in convex programming with linear constraints. In particular, the subdifferential of the value function is the opposite of the set of multipliers associated with a solution. We state two results on the non-emptiness of the subdifferential of the value function. The first one is known and the second one is original since we do not assume any continuity condition on the objective function. We apply these results to different cases arising in mathematical economics. The last part is devoted to the case with equality and inequality constraints. We provide a necessary and sufficient condition for the non-emptiness of the subdifferential of the value function which works even if the interior of the positive cone is empty. Keywords: Convex optimization; Value function; Subdifferential; Multiplier; Convex function properness (search for similar items in EconPapers) Published in Journal of Mathematical Economics, 1996, 25 (1), pp.55-73. ⟨10.1016/0304-4068(95)00717-2⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00187221 DOI: 10.1016/0304-4068(95)00717-2 Access Statistics for this paper More papers in Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL |
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