Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping

Diethard Klatte ()
Additional contact information
Diethard Klatte: IBW, Universität Zürich

Computational Management Science, 2026, vol. 23, issue 1, No 4, 25 pages

Abstract: Abstract This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with parametric linear part. Recall that a multifunction is said to be polyhedral if its graph is the union of finitely many polyhedral convex sets.While this kind of model under a graph-convex polyhedral feasible set mapping F has been well-studied in the literature, we intent to extend these studies to the case of a general polyhedral F. In the general case we show that if the optimal value function is upper semicontinuous,then the optimal set mapping is upper (outer) Lipschitz continuous on its domain, and the optimal value function is Lipschitz continuous on each bounded convex subset of its domain. Moreover, we revisit classical results needed in the proofs and discuss special classes of problems which fit into the model.

Keywords: Polyhedral multifunction; Lipschitz stability; Optimal set mapping; Optimal value function; Upper Lipschitz solution sets; Calmness of optimal values (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10287-025-00547-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:comgts:v:23:y:2026:i:1:d:10.1007_s10287-025-00547-0

Ordering information: This journal article can be ordered from
http://www.springer. ... ch/journal/10287/PS2

DOI: 10.1007/s10287-025-00547-0

Access Statistics for this article

Computational Management Science is currently edited by Ruediger Schultz

More articles in Computational Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().