Parametric Disjunctive Programming: One-Sided Differentiability of the Value Function

M. Gugat
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M. Gugat: University of Trier

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 2, No 4, 285-310

Abstract: Abstract We consider a countable family of one-parameter convex programs and give sufficient conditions for the one-sided differentiability of its optimal value function. The analysis is based on the Borwein dual problem for a family of convex programs (a convex disjunctive program). We give conditions that assure stability of the situation of perfect duality in the Borwein theory. For the reader's convenience, we start with a review of duality results for families of convex programs. A parametric family of dual problems is introduced that contains the dual problems of Balas and Borwein as special cases. In addition, a vector optimization problem is defined as a dual problem. This generalizes a result by Helbig about families of linear programs.

Keywords: Disjunctive programming; families of convex programs; parameteric family of dual problems; efficiency; sensitivity; optimal value function; mixed integer programming (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022603112856

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