Relations between the convexity of a set and the differentiability of its support function. (3rd March 2016)

• Record Type: Journal Article
• Authors: Zălinescu, C.
• Is Part Of: Optimization. Volume 65:Number 3(2016)
• Page Start: 651
• Page End: 670
• Publication Date: 2016-03-03
• Subjects: differentiability of the support function -- convexity -- recession cone -- cost function -- production function; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1044528
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function.