Proximal proper efficiency in set-valued optimization

Arora Ruchi and C.S. Lalitha

Omega, 2005, vol. 33, issue 5, 407-411

Abstract: In this paper, we introduce the concept of cone semilocal convex and cone semilocal convexlike set-valued maps and obtain characterization of these maps in terms of locally star-shaped sets. We derive an alternative theorem involving cone semilocal convexlike set-valued maps under the assumption of closedness of the translation of the image set of the map by the cone under consideration. We introduce proximal proper efficiency for a set-valued optimization problem in finite-dimensional spaces and obtain certain scalarization and Lagrange multiplier theorems. In the end, we consider a Lagrange form of dual and establish weak and strong duality theorems.

Keywords: Set-valued; optimization; Proximal; proper; efficiency; Cone; semilocal; convexlikeness; Lagrange; dual (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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