Convex and convex-like optimization over a range inclusion problem and first applications

Hocine Mokhtar-Kharroubi ()
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Hocine Mokhtar-Kharroubi: Université Oran I

Decisions in Economics and Finance, 2017, vol. 40, issue 1, No 15, 277-299

Abstract: Abstract The paper deals with the minimization of a function over the solution set of a range inclusion problem determined by a multifunction. A strong Lagrange duality is provided first in terms of a quasirelative interior condition and then under a so-called Assumption (S). When the function and the multifunction are convex, we improve this duality under a closed cone condition. The stability analysis is investigated. In addition, if the multifunction is a convex process, then the Fenchel dual is performed in terms of its conjugate. As a first application, we provide a unified approach to the optimization of general discrete inclusions systems; in particular, we improve several results on optimal control, strong Lagrange duality and Fenchel duality for some classes of convex controlled discrete processes.

Keywords: Support function of a multifunction; Optimization over inclusions; Regularity conditions; Strong Lagrange duality; Stabilty; Conjugate duality; Discrete convex systems; Optimal control; 90C25; 49N05; 49N15; 93C05 (search for similar items in EconPapers)
JEL-codes: C02 C14 C3 C44 C55 C61 C62 C67 D58 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10203-017-0190-z

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