Lagrangian Duality in Convex Conic Programming with Simple Proofs

Maria Trnovska and Jakub Hrdina ()
Additional contact information
Jakub Hrdina: Comenius University in Bratislava

SN Operations Research Forum, 2023, vol. 4, issue 4, 1-20

Abstract: Abstract In this paper, we study Lagrangian duality aspects in convex conic programming over general convex cones. It is known that the duality in convex optimization is linked with specific theorems of alternatives. We formulate and prove the strong alternative theorems to the strict feasibility and analyze the relation between the boundedness of the optimal solution sets and the existence of the relative interior points in the feasible set. We also provide sufficient conditions under which the duality gap is zero and the optimal solution sets are unbounded. As a consequence, we obtain several new sufficient conditions that guarantee the strong duality between primal and dual convex conic programs. Our proofs are based only on fundamental convex analysis and linear algebra results.

Keywords: Convex conic programming; Strong duality; Generalized theorems of alternatives (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s43069-023-00279-4 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:snopef:v:4:y:2023:i:4:d:10.1007_s43069-023-00279-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/43069

DOI: 10.1007/s43069-023-00279-4

Access Statistics for this article

SN Operations Research Forum is currently edited by Marco Lübbecke

More articles in SN Operations Research Forum from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().