 Efficiency DualityBruce C. Dieffenbach ()
Chapter 36 in Conjugate Duality in Economic Analysis, 2026, pp 267-272 from Springer Abstract: Abstract We seek conditions for the feasible set to contain an efficient vector or a weakly efficient vector. For a closed, convex cone K in a Euclidean Jordan algebra, the “efficiency alternative” states that exactly one of the following has a solution: 1Some x≫0 belongs toK; 2Some x*≻0 belongs to K∘. The efficiency alternative leads to both efficiency duality and weak-efficiency duality. Consider a nonempty, closed, convex feasible set in a Euclidean Jordan algebra. “Efficiency duality” establishes that three properties are equivalent.EfficiencyThe feasible set contains an efficient vector;Horizon ConeThe horizon cone contains no vector greater than zero;Barrier ConeThe barrier cone contains a positive vector. “Weak-efficiency duality” establishes that three properties are equivalent.Weak EfficiencyThe feasible set contains a weakly efficient vector;Horizon ConeThe horizon cone contains no positive vector;Barrier ConeThe barrier cone contains a vector greater than zero. Invoke the Ekeland variational principle to prove these statements for the barrier cone. The chapter applies these relationships to activity analysis. Date: 2026 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:spr:conchp:978-3-032-21396-9_36 Ordering information: This item can be ordered from DOI: 10.1007/978-3-032-21396-9_36 Access Statistics for this chapter More chapters in Contributions to Economics from Springer |
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