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Proximal proper efficiency for minimisation with respect to normal cones

Published online by Cambridge University Press:  17 April 2009

C. S. Lalitha  and
Ruchi Arora
C. S. Lalitha
Affiliation:
Department of Mathematics, Rajdhani College, University of Delhi, Raja Garden, New Delhi-110 015, India, e-mail: cslalitha@rediffmail.com
Ruchi Arora
Affiliation:
Department of Mathematics, University of Delhi, Delhi - 110 007, India, e-mail: ruchiiq@yahoo.co.in
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This paper is devoted to the study of a new kind of proper efficiency in terms of proximal normal cones for vector minimisation. This new notion called proximal proper efficiency is used to obtain a scalar characterisation when a set related to the criterion set is a nonconvex set. Proximal proper efficiency is related with the well known notions of Benson and Borwein proper efficiency which are defined in the literature in terms of tangent cones. The study is further extended to characterise Benson and Borwein proper efficiency in terms of normal cones assuming convexity of a related set.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 215 - 224
Copyright
Copyright © Australian Mathematical Society 2005

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