Existence of Optimal Quantities and Shadow Prices with No Duality Gap

Anthony Horsley and Andrew Wrobel

Chapter Chapter 6 in The Short-Run Approach to Long-Run Equilibrium in Competitive Markets, 2016, pp 119-135 from Springer

Abstract: Abstract Once a pair of solutions (to a primal-dual programme pair) is found, a direct comparison of their values will show whether there is a duality gap. But there is also a method of checking for a gap at the outset—before solving the programmes. Namely, absence of a duality gap is equivalent to Type One semicontinuity of either optimal value, primal or dual (i.e., to semicontinuity of the primal value w.r.t. the primal parameters, or of the dual value w.r.t. the dual parameters). This well-known result—given in, e.g., [44, Theorem 15] and [36, 7.3.2]—is next stated for the SRP, LRC and SRC optimization programmes.

Keywords: Duality Gap; Dual Value; Dual Parameter; Primal Optimal Value; Dual Banach Lattice (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-33398-4_6

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